Question

A ball is projected from the ground at angle 60 from the ground if ball just clear a wall 5 m from point of projection and falls on the ground 15 m away from it on other side, then height of the wall is nearly equal to

Answer 1

Dear Mandeisepha

As the question says the ball touches the bird at one point.So that point must be the highest point attained by the ball.Because if it was not the highest point then the ball must touch the bird once again i.e when the ball is moving down.

let v be the velocity of ball at the time of projection and θ be the angle of projection

then since horizontal component of velocity of ball = velocity of bird (since they both cover same horizontal distance in same time)

v cos θ =u -eq 1

futher h= v2 sin2 θ/2g

√h= v sinθ /√2g -eq 2

distance on ground where ball strikes=rnage of the projectile=v2 sin 2θ/g=2v2 sin θ cos θ /g

multiply eq 1 and eq 2

u√h=v2sin θ cosθ/√2g

2u√2h/√g=v2 sinθ cosθ*2/g=range

so ball will land on ground at a distance of 2u√2h/√g