Question

Use h=-16t^2+vt+c An acrobat is shot out of a cannon with an initial velocity of 50 ft from 4 ft above the ground. How long will it take him to reach a net that is 10 ft above the ground?

Answer 1

Given data:

The expression for the height is h= -16t^2 +vt+c.

The expression for the velocity is,

`V=-32t+v`

At t=0, the velocity is 50ft/s.

`v=\text{ 50 ft/s}`

At t=0, h= 4ft

`c=4`

The expression for h is,

`h=-16t^2+50t+4`

Substitute 10 ft for h in the above expression.

`\begin{gathered} 10=-16t^2+50t+4 \\ 16t^2-50t+6=0 \\ t=3\text{ s, 0.125 s} \end{gathered}`

Here, two value of times indicates that one in the ascent and second one in the descent.

Thus, the value of time are 3 seconds and 0.125 s.