In the 1999 movie October Sky, Homer Hickam was accused of launching a rocket that started a forest fire. Homer proved his innocence by showing that his rocket could not have flown far enough to reach where the fire started. He used the following reasoning.

(a) Using the fact that a(t) = -32 (see Example 10(a)), find v(t) and s(t), given v(0) V₀ and s(0) = 0. (The initial velocity was unknown, and the initial height was 0 ft.)

(b) Homer estimated that the rocket was in the air for 14 seconds. Use s(14)= 0 to find v₀.

(c) If the rocket left the ground at a 45° angle, the velocity in
the horizontal direction would be equal to v₀, the velocity
in the vertical direction, so the distance traveled horizon-
tally would be v₀t. (The rocket left the ground at a steeper
angle, so this would overestimate the distance from starting
to landing point.) Find the distance the rocket would travel
horizontally during its 14-second flight.

Example 10 (a)

(a) Suppose an object is thrown down from the top of the 1100-ft-tall Willis Tower (formerly known as the Sears Tower) in Chicago. If the initial velocity of the object is -20 ft per second, find s(t), the distance of the object from the ground at time t.