Question

Use a(t) =−32 feet per second squared as the acceleration due to gravity. a ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second. for how many seconds will the ball be going upward?

Answer 1

Since the ball is moving by uniformly accelerated motion, its vertical velocity at time t is given by

`v(t)= v_0 - a t`
where we took upward as positive direction, and where
`v_0` is the initial velocity, a the acceleration and t the time.

The instant at which
`v(t)=0` is the instant when the ball reverses its velocity (from upward to downward). This means that the difference between the time t at which v(t)=0 and the instant t=0 is the total time during which the ball was going upward:

`0=v_0 - at`
By plugging numbers into the equation, we find

`t= (v_0)/(a)= (56 ft/s)/(32 ft/s^2)=1.75 s`