Chapter 1.7, Problem 66E

Physical Science Use the height formula in Example 10 to work the given problems. Note that an object that is dropped (rather than thrown downward) has initial velocity $v_0=0$.

After the baseball in Exercise 65 is dropped, how long does it take for the ball to fall 196 feet? (Hint: How high is the ball at that time?).

65. How long does it take a baseball to reach the dround if it is dropped from the top of a 625-foot-high building? Compare the answer with that in Example 10.

EXAMPLE 10 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

$h=-16t^2+v_{0}t+h_0$,

where $h_0$ is the height of the object when $t=0$ and $v_0$ is the initial velocity at time $t=0$. The value of $v_0$ is taken to be positive if the object moves upward and negative it if moves downward.