Question

A ball is tossed up in the air at an initial rate of 50 ft/sec from 5 ft off the ground.

Answer 1

Answer with Step-by-step explanation:

Since we have given that

Initial velocity = 50 ft/sec = $v_0$

Initial height of ball = 5 feet = $h_0$

a. What type of function models the height (ℎ, in feet) of the ball after tt seconds?

As we know the function for height h with respect to time 't'.

$h(t)=-16t^2+v_0t+h_0\\\\h(t)=-16t^2+50t+5$

b. Explain what is happening to the height of the ball as it travels over a period of time (in tt seconds).

What function models the height, ℎ (in feet), of the ball over a period of time (in tt seconds)?

if it travels over a period of time then time becomes continuous interval . so it will use integration over a period of time

Our function becomes,

$h(t)=\int\limits^t_0 {-16t^2+50t+5} \, dt$