Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Motion in A Plane question

2023 · 8 Apr · Shift 2 · Q55
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Motion in A Plane
  5. /2023 · 8 Apr · Shift 2 · Q55

Motion in A Plane question

2023 · 8 Apr · Shift 2 · Q55

JEE MainPhysicsMotion in A PlaneMCQ+4 / −1
The trajectory of projectile, projected from the ground is given by y=x−x220y=x-\frac{x^{2}}{20}y=x−20x2​. Where xxx and yyy are measured in meter. The maximum height attained by the projectile will be.
  1. A
    10 m
  2. B
    5 m
  3. C
    200 m
  4. D
    10 2\sqrt22​ m
View written solutionFree

Correct answer: B

  1. Given trajectory

    The projectile path is y=x−x220y=x-\frac{x^2}{20}y=x−20x2​

    This is a downward-opening parabola of the form y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c with a=−120,b=1,c=0.a=-\frac{1}{20},\quad b=1,\quad c=0.a=−201​,b=1,c=0.

  2. Maximum height occurs at the vertex

    For a parabola y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c, the xxx-coordinate of the vertex is xv=−b2a.x_v=-\frac{b}{2a}.xv​=−2ab​.

    Substituting: xv=−12(−120)=10.x_v=-\frac{1}{2\left(-\frac{1}{20}\right)}=10.xv​=−2(−201​)1​=10.

  3. Find the corresponding yyy value

    Put x=10x=10x=10 into the trajectory equation: y=10−10220=10−10020=10−5=5.y=10-\frac{10^2}{20}=10-\frac{100}{20}=10-5=5.y=10−20102​=10−20100​=10−5=5.

    So the maximum height is 5 m.5\text{ m}.5 m.

  4. Check options

    • A: 10 m10\text{ m}10 m ❌
    • B: 5 m5\text{ m}5 m ✅
    • C: 200 m200\text{ m}200 m ❌
    • D: 102 m10\sqrt{2}\text{ m}102​ m ❌

Therefore, the correct option is B.

PreviousNext

More from Motion in A Plane

  • The range of the projectile projected at an angle of 15 ∘ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45 ∘ with horizontal, then its range will be2023 · MCQ
  • Two projectiles are projected at 30∘ and 60∘ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:2023 · MCQ
  • A projectile fired at 30∘ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is ​m s−1…2023 · Numerical
  • A projectile is projected at 30∘ 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/s2 )2023 · 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 · MCQ
  • Two objects are projected with same velocity 'u' however at different angles α and β with the horizontal. If α+β=90∘, the ratio of horizontal range of the first object to the 2nd object will be :2023 · MCQ
  • The initial speed of a projectile fired from ground is u. At the highest point during its motion, the speed of projectile is 23​​u. The time of flight of the projectile is :2023 · 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 1 km, he reaches a point 750 m down the stream on the opposite bank.…2023 · Numerical