Question

Carl
jumps out of a plane and, after opening his parachute,
reaches a constant terminal velocity of 25 m/s. When he
is 1200 m above the ground, Mitch, standing directly
below Carl, launches a pumpkin straight up into the air
at Carl. The pumpkin has an initial velocity of 145 m/s.
(a) How much time does Carl have until it’s time for
pumpkin pie (IOW, until it smashes into Skid)?
(b) Assuming Carl does not have his wits about him, at
what location above the ground will the pumpkin
intersect with him?

Answer 1

constant terminal velocity of carl, v_t = 25 m/s

distance of carl above ground, when mike launches the pumpkin, d = 1200 m

initial velocity of the pumpkin, u_p = 145 m/s

Let Carl intersect the pumkin after travelling a distance x.

Let t be the time when they meet.

x = v_tt --(1)

1200 - x = u_pt - (1/2)gt² --(2)

maximum height the pumpkin can reach (h), and the time teken to cover it (t') can be calculated as follows:

h = (v_p² - u_p²)/2g = 1072.704 m

t' = u_p/g = 14.796 s; (from eqn v_p = u_p - gt')

a.

substituting (1) in (2)

1200 - v_tt = u_pt - (1/2)gt²

=> 1200 - 25t = 145t - 4.9t²

=> 4.9t² - 145t - 25t + 1200 = 0

=> 4.9t² -170t + 1200 = 0

t = 24.831 or t = 9.862

Since the pumpkin starts falling down after 14.796 s, the time for it to hit Carl should be less than this.

Therefore t = 9.862 s

b.

x = v_tt = 25 * 9.862 = 246.55

1200 - x = 1200 - 246.55 = 953.45

The pumpkin intersects Carl at a distance of 953.45 m above the ground.