126k views
5 votes
The height equation d = 16t² + h0 describes an object's height in feet above the ground t seconds after it's dropped from

a starting height of h0. Johnson throws a rock from the top of a
hill, which measures 200 feet in height. How long does it take the
rock to reach the ground? Round your answer to the nearest
tenth of a second.

1 Answer

3 votes

Answer:

3.5 seconds

Explanation:

d = 16t^2 + h0

For a falling object, the equation should read:

d(t) = -16t^2 + h(0) [The 16 should have a minus sign, to account for the fact the ball is falling]. h0 we'll assume is actually h(0), or the height at time = 0 (the start). d(t) is the distance from Earth as a function of time, t)

The expression for a free falling object is d = (1/2)gt^2, where g is the acceleration due to gravity and t is time. Since the distance is given in feet, and since (1/2)g = -16, we can assume g is -32 feet/sec^2, the English value for gravity. At time = 0, h is 200 feet (dropped at the start from 200 feet).

Let's assume the term h0 is actually h(t) where h is the height and t is the time, in seconds. h(0) would mean the height at time = 0 seconds, the starting position. h(0) here is 200 feet.

d(t) = -16t^2 + h(0)

d(t) = -16t^2 + 200

We want the value of t such that d(t) = 0 (reaches ground)

d(t) = -16t^2 + 200

0 = -16t^2 + 200 for d(t) = 0

16t^2 = 200

t^2 = 12.5

t = 3.5 seconds

User Sherlock
by
7.9k points