You are standing on a hotel balcony 30 feet up from the ground. You want to thro

Question

You are standing on a hotel balcony 30 feet up from the ground. You want to throw your key to someone standing outside the hotel on the ground. You throw it angled upward with an initial velocity of 55 ft/sec. Assume that the acceleration due to gravity is -32 ft/sec/sec.

A) Find the position function in terms of time, t.

B) Your friend misses catching the key, and it falls to the ground. How many seconds does it take to reach the ground?

C) After 3 seconds, how high in the air is the key?

D) How long has it been if the key is 40 feet in the air?

E) When is the velocity 25 ft/sec?

F) Plot your function using a sensible interval. Does the appearance of the plot make sense based on your above answers? Why or why not?

Explanation / Answer

a = -32 ft/s2 = constant
v = u + at
s = vt + 1/2(at2) + u
We know s = 40, u = 30, v = 55ft/s , a = -32 ft/s2
40 = 30 + 55t - 32/2t2
16t2 - 55t + 10 = 0............................(1)
The key will be in air at 40 feet at t = .193 sec
and then on the way back down, t = 3.24 sec

For C, put t=3 in eq 1

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