Hello sir/ma`am please help me in this question...................A ball is thrown from a point on the ground at some angle of projection.At the same time , a bird starts from a point directly above this point of projection at a height (h) horizontally with speed (u). given that in its flight the ball just Touches the bird at one point.find the distance on ground where the ball strike

Here, clearly the horizontal component of the velocity with which the ball is projected is equal to the velocity of the bird because they cover equal horizontal distance in equal time (ball touches the bird), Therefore Vx(horizontal) = uThe distance on ground where ball strikes, Range=Vx × t(time of flight)..... (i) Also we know, t=2Vy/g........ (ii) (equation of projectile) and Vy=[2gh]^1/2...... (iii) (derived v^2 =u^2 +2as keeping u=Vy, v=0, s=h, a=-g because at topmost point i. e. h v=0 ; its is also an equation in projectile) On substituting (iii) in (ii) t={2[2gh]^2}/g.....(iv)substituting (iv) in (i) Range=u/g{2[2gh]^2}. This is the distance on the ground where the ball strikes.

Here, clearly the horizontal component of the velocity with which the ball is projected is equal to the velocity of the bird because they cover equal horizontal distance in equal time (ball touches the bird), Therefore Vx(horizontal) = uThe distance on ground where ball strikes, Range=Vx × t(time of flight)..... (i) Also we know, t=2Vy/g........ (ii) (equation of projectile) and Vy=[2gh]^1/2...... (iii) (derived v^2 =u^2 +2as keeping u=Vy, v=0, s=h, a=-g because at topmost point i. e. h v=0 ; its is also an equation in projectile) On substituting (iii) in (ii) t={2[2gh]^1/2/g.....(iv)substituting (iv) in (i) Range=u/g{2[2gh]^1/2}. This is the distance on the ground where the ball strikes.