word problem

Question

The height in feet, h, reached by a projectile after t seconds is given by the function:

h(t) = -16t^2 + 110t + 5

When will the projectile hit ground level?

Round your answer to 2 decimal places.

Answer 1

This projectile had an initial velocity of 110 ft/sec

and an initial height of 5 ft

 

We want to know the amount of time that passes

before it hits the ground.. which is a height of 0

 

-16t² + 110t + 5 = 0

 

using quadratic equation t = (-b±√(b²-4ac))/2a

a = -16, b = 110, c = 5

 

t = [-110 ±√(110²-4(-16)(5))]/2(-16)

 

t = (-110±√(12420))/(-32)

 

t = (-110 ± 111.445)/(-32)

 

t = 1.445/(-32)   or   t = -221.445/(-32)

t = -0.04516             t = 6.92

 

Discarding the negative, it will strike the ground

in approximately 6.92 seconds