Question

A boy on a trolley is sliding down on a smooth incline having inclination angle 37" He throws a ball such that he catches it back after time 5 sec. With what velocity was the ball thrown by the boy relative to himself?​

Answer 1

here is the answer, it is not written by me.

the credit goes to abhi178

Answer 2

Given info : A boy  on a trolley is sliding down on smooth incline having inclination angle 37°. he throws a ball such that he catches it back after time 5sec.

To find : the velocity of the ball thrown by the boy relative to himself is ...

solution : first we have to find the angle at which ball has thrown.

let the angle at which ball is thrown, is α.

velocity of the boy with respect to ground is u and velocity of ball with respect to boy is v.

component of velocity of ball along plane = u + vcosα

component of velocity of ball perpendicular to plane = vsinα

we know, boy can the ball only when distance covered by the boy and the distance covered by the ball along plane are same.

i.e., distance covered by the boy = distance covered by the ball

⇒ ut + 1/2gsin37°t² = (u + vcosα)t + 1/2gsin37°t²

⇒ cosα = 0 = cos90°

⇒ α = 90°

so the ball is thrown vertically upwards, isn't it ?

we also know that the net displacement of ball with respect to plane is zero because the the same position in vertical direction.

 ⇒ 0 = (vsin90°)t + 1/2(-gcos37°)t²

⇒ v = gcos37°t/2

using cos37° = 4/5 , t = 5sec and g = 10m/s²

so, v = (10 × 4/5 × 5)/2 = 20m/s

therefore the velocity of the ball thrown by the boy relative to himself is 20 m/s.