Question

A video game uses the quadratic equation h equals space minus 16 t to the power of 2 space end exponent plus space 64 t space plus space 190 to determine the height h in feet of an object above the ground after t seconds.

Answer 1

Explanation:

Given

h varies as

`h=-16t^2+64t+190`

Above h represents the height of object at any instant t

For example at t=0

h=190 ft

At t=1 s

h=-16+64+190=238 ft

For maximum height differentiate h w.r.t time

`\frac{\mathrm{d} h}{\mathrm{d} t}=-16* 2* t+64`

Put
`\frac{\mathrm{d} h}{\mathrm{d} t}=0` to get maximum height

`-32t+64=0`

t=2 i.e. at t= 2 s h is maximum

h at t=2 s

`h=-16* 2^2+64* 2+190=254 m`