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Motion in A Plane

85 questions · Physics · JEE Main

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Motion in A Plane

Motion in A Plane

85 questions · Physics · JEE Main

A river is flowing from west to east direction with speed of $9 km h^{- 1}$ . If a boat capable of moving at a maximum speed of $27 km h^{- 1}$ in still water, crosses the river in half a minute, while…2025 · 2 Apr · Shift 1 · Q54 · MCQ
The angle of projection of a particle is measured from the vertical axis as $ϕ$ and the maximum height reached by the particle is $h_{m}$ . Here $h_{m}$ as function of $ϕ$ can be presented as2025 · 3 Apr · Shift 1 · Q54 · MCQ
A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u ^{2}}{25 g}$ , where value of $n$ is: (Given, ' $g$ ' is the…2025 · 3 Apr · Shift 2 · Q67 · MCQ
Two projectiles are fired from ground with same initial speeds from same point at angles $(4 5^{\circ} + α)$ and $(4 5^{\circ} - α)$ with horizontal direction. The ratio of their times of flights is2025 · 7 Apr · Shift 1 · Q62 · MCQ
A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where…2025 · 7 Apr · Shift 2 · Q53 · MCQ
Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_{1}$ and $T_{2}$ are the total flying times of first…2025 · 8 Apr · Shift 2 · Q64 · MCQ
A particle is projected at an angle of $3 0^{\circ}$ from horizontal at a speed of $60 m / s$ . The height traversed by the particle in the first second is $h_{0}$ and height traversed in the last second, before it…2025 · 22 Jan · Shift 1 · Q74 · Numerical
A ball of mass 100 g is projected with velocity $20 m / s$ at $6 0^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is2025 · 22 Jan · Shift 2 · Q68 · MCQ
An object of mass ' m ' is projected from origin in a vertical xy plane at an angle $4 5^{\circ}$ with the $x -$ axis with an initial velocity $v_{0}$ . The magnitude and direction of the angular momentum of the object with…2025 · 24 Jan · Shift 1 · Q51 · MCQ
The position vector of a moving body at any instant of time is given as $r = (5 t^{2} \hat{i} - 5 t \hat{j}) m$ . The magnitude and direction of velocity at $t = 2 s$ is,2025 · 24 Jan · Shift 2 · Q67 · MCQ
Two projectiles are fired with same initial speed from same point on ground at angles of $(4 5^{\circ} - α)$ and $(4 5^{\circ} + α)$ , respectively, with the horizontal direction. The ratio of their maximum heights attained is :2025 · 29 Jan · Shift 1 · Q58 · MCQ
The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer…2025 · 29 Jan · Shift 1 · Q68 · Numerical
The co-ordinates of a particle moving in $x$ - $y$ plane are given by : $x = 2 + 4 t, y = 3 t + 8 t^{2}$ . The motion of the particle is :2024 · 4 Apr · Shift 1 · Q71 · MCQ
The maximum height reached by a projectile is $m$ . If the initial velocity is halved, the new maximum height of the projectile is $m$ .2024 · 5 Apr · Shift 2 · Q86 · Numerical
The angle of projection for a projectile to have same horizontal range and maximum height is :2024 · 8 Apr · Shift 2 · Q75 · MCQ
A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of $2 M$ from the foot of the tower. A body of mass $\frac{v}{2}$ thrown at a velocity $\frac{v}{2}$ …2024 · 8 Apr · Shift 2 · Q90 · Numerical
Position of an ant ( $S$ in metres) moving in $Y$ - $Z$ plane is given by $S = 2 t^{2} \hat{j} + 5 \hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t = 1 s$ will be…2024 · 27 Jan · Shift 1 · Q61 · MCQ
A particle starts from origin at $t = 0$ with a velocity $5 \hat{i} m / s$ and moves in $x - y$ plane under action of a force which produces a constant acceleration of $(3 \hat{i} + 2 \hat{j}) m / s^{2}$ . If…2024 · 27 Jan · Shift 1 · Q81 · Numerical
A ball rolls off the top of a stairway with horizontal velocity $u$ . The steps are $0.1 m$ high and $u$ wide. The minimum velocity $u$ with which that ball just hits the step 5 of the stairway will be $x ms^{- 1}$ …2024 · 29 Jan · Shift 1 · Q89 · Numerical
Projectiles A and B are thrown at angles of $4 5^{\circ}$ and $6 0^{\circ}$ with vertical respectively from top of a $v_{A} : v_{B}$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $v_{A} : v_{B}$ …2024 · 30 Jan · Shift 2 · Q77 · MCQ
A child stands on the edge of the cliff $5 ms^{- 1}$ above the ground and throws a stone horizontally with an initial speed of $5 ms^{- 1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be…2023 · 1 Feb · Shift 1 · Q53 · MCQ
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : When a body is projected at an angle $4 5^{\circ}$ , it's range is maximum. Reason R : For maximum range, the value of $sin 2 θ$ …2023 · 6 Apr · Shift 1 · Q46 · MCQ
Two projectiles A and B are thrown with initial velocities of $40 m / s$ and $60 m / s$ at angles $3 0^{\circ}$ and $6 0^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively…2023 · 8 Apr · Shift 1 · Q59 · MCQ
The trajectory of projectile, projected from the ground is given by $y = x - \frac{x ^{2}}{20}$ . Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.2023 · 8 Apr · Shift 2 · Q55 · MCQ
The range of the projectile projected at an angle of 15 $^{\circ}$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45 $^{\circ}$ with horizontal, then its range will be2023 · 10 Apr · Shift 1 · Q53 · MCQ
Two projectiles are projected at $3 0^{\circ}$ and $6 0^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:2023 · 10 Apr · Shift 2 · Q45 · MCQ
A projectile fired at $3 0^{\circ}$ to the ground is observed to be at same height at time $5 s$ and after projection, during its flight. The speed of projection of the projectile is $m s^{- 1}$ …2023 · 11 Apr · Shift 1 · Q69 · Numerical
A projectile is projected at $3 0^{\circ}$ from horizontal with initial velocity $40 ms^{- 1}$ . The velocity of the projectile at $t = 2 s$ from the start will be : (Given $g = 10 m / s^{2}$ )2023 · 11 Apr · Shift 2 · Q54 · MCQ
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :2023 · 24 Jan · Shift 1 · Q58 · MCQ
Two objects are projected with same velocity 'u' however at different angles $α$ and $β$ with the horizontal. If $α + β = 9 0^{\circ}$ , the ratio of horizontal range of the first object to the 2nd object will be :2023 · 25 Jan · Shift 2 · Q55 · MCQ
The initial speed of a projectile fired from ground is $u$ . At the highest point during its motion, the speed of projectile is $\frac{3}{2} u$ . The time of flight of the projectile is :2023 · 31 Jan · Shift 1 · Q48 · MCQ
The speed of a swimmer is $4 km h^{- 1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $750 m$ , he reaches a point $750 m$ down the stream on the opposite bank.…2023 · 31 Jan · Shift 1 · Q68 · Numerical
Two bodies are projected from ground with same speeds $40 ms^{- 1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $6 0^{\circ}$ , with…2023 · 31 Jan · Shift 2 · Q66 · Numerical
A projectile is projected with velocity of 25 m/s at an angle $θ$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $θ$ will be :…2022 · 24 Jun · Shift 1 · Q48 · MCQ
A body is projected from the ground at an angle of 45 $^{\circ}$ with the horizontal. Its velocity after 2s is 20 ms $-$ 1. The maximum height reached by the body during its motion is m. (use g = 10 ms $-$ 2)2022 · 24 Jun · Shift 2 · Q65 · Numerical
A ball is projected from the ground with a speed 15 ms $-$ 1 at an angle $θ$ with horizontal so that its range and maximum height are equal, then 'tan $θ$ ' will be equal to :2022 · 25 Jul · Shift 2 · Q60 · MCQ
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range…2022 · 25 Jun · Shift 2 · Q46 · MCQ
Two projectiles thrown at $3 0^{\circ}$ and $4 5^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :2022 · 26 Jul · Shift 1 · Q62 · MCQ
If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y = 5 x (1 - x)$ . The $y$ component vector of the initial velocity is $\hat{j}$ . ( $Take$ …2022 · 26 Jul · Shift 1 · Q64 · Numerical
Two projectiles are thrown with same initial velocity making an angle of $4 5^{\circ}$ and $3 0^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be :2022 · 26 Jul · Shift 2 · Q40 · MCQ
A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms $-$ 1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $θ$ with the horizontal, to hit the jet. If…2022 · 26 Jun · Shift 1 · Q59 · Numerical
A ball of mass m is thrown vertically upward. Another ball of mass $θ$ is thrown at an angle $θ$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls…2022 · 27 Jul · Shift 1 · Q72 · Numerical
A projectile is launched at an angle ' $α$ ' with the horizontal with a velocity 20 ms $-$ 1. After 10 s, its inclination with horizontal is ' $β$ '. The value of tan $β$ will be : (g = 10 ms $-$ 2).2022 · 27 Jun · Shift 1 · Q42 · MCQ
A girl standing on road holds her umbrella at 45 $^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15 $2$ kmh $-$ 1, the rain drops hit her head vertically. The speed of rain…2022 · 27 Jun · Shift 1 · Q43 · MCQ
At time $t = 0$ a particle starts travelling from a height $7 \overset{z}{^} cm$ in a plane keeping z coordinate constant. At any instant of time it's position along the $\overset{x}{^}$ and $\overset{y}{^}$ directions are defined as $3 t$ and…2022 · 28 Jul · Shift 2 · Q41 · MCQ
An object is projected in the air with initial velocity u at an angle $θ$ . The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of…2022 · 29 Jul · Shift 1 · Q67 · Numerical
A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?2022 · 29 Jun · Shift 2 · Q61 · MCQ
At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms $-$ 2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of…2022 · 30 Jun · Shift 1 · Q42 · MCQ
Two projectiles P1 and P2 thrown with speed in the ratio $3$ : $2$ , attain the same height during their motion. If P2 is thrown at an angle of 60 $^{\circ}$ with the horizontal, the angle of projection of P1 with horizontal will be :2022 · 30 Jun · Shift 1 · Q45 · MCQ
The ranges and heights for two projectiles projected with the same initial velocity at angles 42 $^{\circ}$ and 48 $^{\circ}$ with the horizontal are R1, R2 and H1, H2 respectively. Choose the correct option :2021 · 1 Sep · Shift 2 · Q51 · MCQ
A mosquito is moving with a velocity $v = 0.5 t^{2} i + 3 t j + 9 k$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after 2 s?2021 · 16 Mar · Shift 2 · Q51 · MCQ
A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just…2021 · 16 Mar · Shift 2 · Q68 · Numerical
A person is swimming with a speed of 10 m/s at an angle of 120 $^{\circ}$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is …2021 · 18 Mar · Shift 1 · Q66 · Numerical
A butterfly is flying with a velocity $42$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :2021 · 20 Jul · Shift 1 · Q51 · MCQ
A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :2021 · 26 Aug · Shift 2 · Q56 · MCQ
The trajectory of a projectile in a vertical plane is y = $α$ x $- β$ x2, where $α$ and $β$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection.…2021 · 26 Feb · Shift 2 · Q59 · MCQ
A player kicks a football with an initial speed of 25 ms $-$ 1 at an angle of 45 $^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms $-$ 2)2021 · 27 Aug · Shift 2 · Q56 · MCQ
A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30 $^{\circ}$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $θ$ with the line AB should be … Includes diagram2021 · 27 Jul · Shift 2 · Q67 · Numerical
A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?2021 · 31 Aug · Shift 1 · Q46 · MCQ
Starting from the origin at time t = 0, with initial velocity 5 $j$ ms-1 , a particle moves in the x-y plane with a constant acceleration of $(10 i + 4 j)$ ms-2. At time t, its coordinates are (20…2020 · 4 Sep · Shift 1 · Q64 · MCQ
A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distanced (point B) from A (see figure) sees it at an angle 45o with respect to the vertical. When the balloon climbs… Includes diagram2020 · 5 Sep · Shift 1 · Q57 · MCQ
When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + $β$ …2020 · 6 Sep · Shift 2 · Q46 · MCQ
A particle is moving along the x-axis with its coordinate with the time 't' given be x(t) = 10 + 8t – 3t2. Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t3. At t = 1s, the speed of the…2020 · 8 Jan · Shift 1 · Q48 · Numerical
A particle moves such that its position vector $r (t) = cos ω t i + sin ω t j$ where $ω$ is a constant and t is time. Then which of the following statements is true for the…2020 · 8 Jan · Shift 2 · Q39 · MCQ
A particle starts from the origin at t = 0 with an initial velocity of 3.0 $i$ m/s and moves in the x-y plane with a constant acceleration $(6 i + 4 j)$ m/s2 . The x-coordinate of the particle at…2020 · 9 Jan · Shift 2 · Q53 · MCQ
Ship A is sailing towards north-east with velocity $v \to = 30 i \land + 50 j \land$ km/hr where $i \land$ points east and $j \land$ , north. Ship B is at…2019 · 8 Apr · Shift 1 · Q61 · MCQ
The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?2019 · 9 Apr · Shift 1 · Q64 · MCQ
A particle is moving with a velocity $v = K (y i + x j),$ where K is a constant. The general equation for its path is :2019 · 9 Jan · Shift 1 · Q52 · MCQ
The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos $ω$ t y = a sin $ω$ t and z = a $ω$ t The speed of the particle is :2019 · 9 Jan · Shift 2 · Q72 · MCQ
A plane is inclined at an angle $α$ = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms–1 , from the base of the plane, making an angle $θ$ = 15° with respect to the plane as shown in the figure.… Includes diagram2019 · 10 Apr · Shift 2 · Q45 · MCQ
Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the…2019 · 10 Jan · Shift 1 · Q65 · MCQ
The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2 . If it were launched at an angle $θ$ 0 with speed v0 then (g = 10 ms–2) :2019 · 12 Apr · Shift 1 · Q57 · MCQ
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product…2019 · 12 Apr · Shift 1 · Q66 · MCQ
Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct ?2019 · 12 Apr · Shift 2 · Q61 · MCQ
A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :2019 · 12 Jan · Shift 1 · Q66 · MCQ
A man in a car at location Q on a straight highway is moving with speed $υ$ . He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that… Includes diagram2018 · 15 Apr · Shift 2 · Q56 · MCQ
A projectile is given an initial velocity of $(i + 2 j)$ m/s, where $i$ is along the ground and $j$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:2013 · Shift 0 · Q74 · MCQ
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be2012 · Shift 0 · Q66 · MCQ
A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :2011 · Shift 0 · Q77 · MCQ
A particle is moving with velocity $v = k (y i + x j)$ , where K is a constant. The general equation for its path is2010 · Shift 0 · Q77 · MCQ
A particle has an initial velocity $3 i + 4 j$ and an acceleration of $0.4 i + 0.3 j$ . Its speed after 10 s is:2009 · Shift 0 · Q75 · MCQ
A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is2005 · Shift 0 · Q171 · MCQ
A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two cases, then the product of the two time of flights is directly proportional to2004 · Shift 0 · Q186 · MCQ
A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed $\frac{v _{0}}{2}$ to catch the ball. Will the person be able to catch the…2004 · Shift 0 · Q189 · MCQ
A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $3 0^{\circ}$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? $[g = 10 m / s^{2}, sin 3 0^{\circ} = \frac{1}{2}, cos 3 0^{\circ} = \frac{3}{2}]$ …2003 · Shift 0 · Q173 · MCQ