Problem #01: Proiectile Motion boy kicks oyt a ball from the top of a ill which

Question

Problem #01: Proiectile Motion boy kicks oyt a ball from the top of a ill which is 100m tall in height (h), in a straight forward direction. The ball flies off the hill and eventually strikes down the plain at d distance (d), 6 Km from the base of the hill. Assume that the ball flies off the hill in a semi-parabolic trajectory in a free-fall motion 0 Write down an appropriate diagram for its motion, and all corresponding initial parameters pertaining to the kinematics of the ball that is kicked out from the hill-top? Determine the initial velocity and time-of-flight of the ball as it leaves the hill top? Determine the direction of the ball right before it hits the ground? a) b) c)

Explanation / Answer

height of hill, h = 1000 m
distance from the hill, horizontal d = 6000 m

a. so the ball is given initial velocity vo ( which is horizontal)
   time taken to fall down be t
   then initial vertical velocity = 0
   so, h = 0.5gt^2
   and d = vo*t
   t = sqroot(2h/g)
   hence vo = d/sqroot(2h/g)

b. time of flight t = sqroot(2h/g) = sqroot(2*1000/9.81) = 14.278 s
   vo = 420.214231 m/s

c. right before the ball hits the ground
   vx = vo = 420.214 m/s
   vy = -gt = -9.81*14.278 = -140.067 m/s
   direction = arctan(vy/vx) = 18.4344 deg below the horizontal

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