If an arrow is shot upward...?

Question

If an arrow is shot upward on the moon with a velocity of 50 m/s, its height (in meters) after t seconds is given by H = 50t - 0.83t^2.

(a) Find the velocity of the arrow after one second.
(b) Find the velocity of the arrow when t = a.
(c) When will the arrow hit the moon?
(d) With what velocity will the arrow hit the moon?

Answer 1

a) velocity: take derivative,
H'(t) = 50 - 1.66 t
H'(1) = 50 - 1.66 * 1 = 48.34 m/s

b) H'(a) = 50 - 1.66 a

c) solve H(t) = 0
50 t - 0.83 t^2 = 0
(50 - 0.83 t) t = 0
50 - 0.83 t = 0 ... OR ... t = 0
t = 60 s ... OR ... t = 0 s
(second solution is launch)

d) H'(60) = 50 - 1.66 * 60 = -50 m/s
or, by physical intuition, its final speed is equal to its initial speed, but in opposite direction

Answer 2

I'm, ... I'm getting a headache. The arrow would break so the answer is meaningless.