1) A rock is thrown at an angle of 35 degrees above the horizontal at a speed v

Question

1) A rock is thrown at an angle of 35 degrees above the horizontal at a speed vo. The rock reaches a maximum height of 15m, then hits the ground at the same height it was thrown from. What height would the rock reach if it were thrown straight upward with speed vo?

2) A rifle is used to shoot two bullets at a target, using identical cartridges. For the first shot, the rifle is aimed parallel to the ground and directly at the center of the target. The rifle is placed 100m from the target. The bullet strikes the target slightly below the center. For the second shot, the rifle is similarly aimed, however the rifle is placed 300m from the target. The second bullet hits the target below the first bullet. If the muzzle velocity of the gun is 800m/s, what is the distance between the two bullets on the target?

Explanation / Answer

1) so max height when vy = 0

vy^2 = v0y^2 + 2 a y

0 = (v0*sin(theta)) - 2 g y

y = v0^2 sin(theta)^2/(2 g)

15 = v^2*sin(35 degrees)^2/(2*9.81)

v=29.9 m/s

now if straight up theta = 90

y = 29.9^2/(2*9.81)= 45.6 m

2)

first case:

x = v t
t = 100/800 = 1/8 s

y = -1/2 a t^2 = -0.5*9.81*(1/8)^2=-0.0766 m

second case:
t = 300/800 = 3/8 s

y = -0.5*9.81*(3/8)^2 = -0.6898 m

so dy = -0.0766+0.6898=0.6132 m

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