Physical Science Use the height formula in Example 1 to work the given problem. Note that...

Physical Science Use the height formula in Example 1 to work the given problem. 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 625-foot-high building? Compare the answer with that in Example 1.

Example 1

Physical Science 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

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 to be positive if the object moves upward and negative if it moves downward. Suppose that a golf ball is thrown downward from the top of a 625-foot high building with an initial velocity of 65 feet per second. How long does it lake to reach the ground?

Solution In this case, h0 = 625 (the height of the building) and v0 = −65 (negative because the ball is thrown downward). The object is on the ground when h = 0, so we must solve the equation

Using the quadratic formula and a calculator, we see that

Only the positive answer makes sense in this case. So it takes about 4.54 seconds for the ball to reach the ground.