Question

A coin is tossed upward with an initial velocity of 32 feet per second from a height of 16 feet above the ground.The equation giving the object's height h at any time t is h = 16 + 32t - 16t^2. Does the object ever reach a height of 32 feet?(Select an answer No or Yes! If so, when? (Answer "dne" if it does not.)It reaches 32 feet after___seconds.

Answer 1

Given:

`h=16+32t-16t^2`

To get the maximum height, we differentiate. At maximum height, the velocity is zero.

Hence,

`\begin{gathered} (dh)/(dt)=32-32t \\ when\text{ }(dh)/(dt)=0, \\ 0=32-32t \\ 32t=32 \\ t=(32)/(32) \\ t=1sec \end{gathered}`

Thus, substitute t = 1 into the equation;

`\begin{gathered} h=16+32(1)-16(1^2) \\ h=16+32-16 \\ h=32ft \end{gathered}`

Since the maximum height is 32 feet, then the object reaches 32feet after 1 second.