Chapter 1.7, Problem 67E

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 $v_0=0$.

You are standing on a cliff that is 200 feet high. How long will it take a rock to reach the ground if

(a) you drop it?

(b) you throw it downward at an initial velocity of 40 feet per second?

(c) How far does the rock fall in 2 seconds if you throw it downward with an initial velocity of 40 feet per second?

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.