Question

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

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

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`