In Exercise, use the height equation in Example 1. Note that an object that is dropped (ra...

In Exercise, use the height equation in Example 1. Note that an object that is dropped (rather than thrown downward) has initial velocity v0 = 0.

How long does it take a baseball to reach the ground if it is dropped from the top of a 640-foot-high building? Compare with Example 1.

EXAMPLE 1

If an object is thrown upward, dropped, or thrown downward and travels in a straight line subject only to gravity (with wind resistance ignored), the height h of the object above the ground (in feet) after t seconds is given by

 h = −16t2 + v0t + h0,

where h0 is the height of the object when t = 0 and v0 is the initial velocity at time t = 0. The value of v0 is taken as positive if the object moves upward and negative if it moves downward. If a baseball is thrown down from the top of a 640-foot-high building with an initial velocity of 52 feet per second, how long does it take to reach the ground?

SOLUTION

In this case, v0 is −52 and h0 is 640, so that the height equation is

 h = −16t2 − 52t + 640.

The object is on the ground when h = 0, so we must solve the equation

 0 = −16t2 − 52t + 640.

Using the quadratic formula and a calculator, we see that

Only the positive answer makes sense in this case. So it takes about 4.9 seconds for the baseball to reach the ground.