Question

6 A ball is thrown from ground-level with speed v at an angle 0 to the horizontal (0 < 0 < п /2). (a) When and where does the ball hit the ground? (b) Now suppose that the ground is sloped in the shape y(x)= Ar as pictured below. The ball is thrown as before from the origin. When and where does the ball hit the ground? y (c) Now suppose the ground takes the form of the hill pictured below. The peak of the hill is a height H off the ground, located a horizontal distance L from the origin. Determine the speed v and angle 0 such that the ball will just graze the peak of the hill y m x (ml

Answer 1

Equation of trajectory of projecile γ- xtα θ au ces u-initial ped ravity Hccelenation du to hit ground a) for ball fo tan 9 2uco utsin2o 2using BA &

Now as per given in the question the trajectory for the body should intercept the given conditions i.e. it should touch the ground y=Ax hence putting y=Ax in equation will give the cordinates of the point where the trajectory intersects the plank and hence we will get the point of contact of ball with the plank.

x tan - 9x Qu2cesag tan &- A 2 taking Cemm on, (tan A uce Kipe at H tan& (L tan& - H)2 ucsa 2 gh 2ces20 (L tan-H)