Question

A model rocket is launched with an initial upward velocity 39M/S. The rockets height H (in meters) after t seconds is given by the following. h=39t-5t2Find all values for which the rockets height is 22 meters.

Answer 1

Given:

$h=39t-5t^2$

It is given that h=22m,

$22=39t-5t^2$$5t^2-39t+22=0$$t=\frac{39\pm\sqrt[]{39^2-4(5)(22)}}{2(5)}$$t=\frac{39\pm\sqrt[]{1521-440}}{10}$$t=\frac{39\pm\sqrt[]{1081}}{10}$$t=\frac{39\pm32.88}{10}$$t=\frac{39+32.88}{10},\frac{39-32.88}{10}$$t=\frac{71.88}{10},\frac{6.12}{10}$$t=7.188,0.612$

The values for the rockets height is 22m are 0.61 seconds and 7.19 seconds.