Question

A model rocket is launched with an initial upward velocity of 215 ft/s. The rocket's height h (in feet) after t seconds is given by the following.

h=215t-16t^2

Find all values of t for which the rocket's height is 97 feet.

Answer 1

t=12.97 seconds

t=0.47 seconds

Explanation:

Given :

A model rocket is launched with an initial upward velocity of 215 ft/s.

The rocket's height h (in feet) after t seconds :
`h=215t-16t^2`

To Find:

Find all values of t for which the rocket's height is 97 feet.

Solution :

`h=215t-16t^2`

Since we are given that height = 97 feet

`97=215t-16t^2`

`16t^2-215t+97=0`

Using quadratic formula :
`t=(-b\pm√(b^2-4ac))/(2a)`

a = 16

b = -215

c = 97

`t=(215\pm√((-215)^2-4*16* 97))/(2* 16)`

`t=(215\pm√(40017))/(32)`

t = 12.970077983916697359451253891375

t = 0.46742201608330264054874610862542

Thus all values of t for which the rocket's height is 97 feet:

t=12.97 seconds

t=0.47 seconds