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

Answer:

Step-by-step 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

$\frac{\mathrm{d} h}{\mathrm{d} t}=-16\times 2\times t+64$

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

$h=-16\times 2^2+64\times 2+190=254 m$