Algebra 2 Word Problem

Question

an employee a local stadium is launching T-shirts from a T-shirt canon into the crowded during the intermission of the football game the height h in feet of the T-shirt after t seconds, can be modeled by h = -16t² +96t +4 if no one catches the shirt and the shirt lands on the ground, when would it hit the ground?

Answer 1

Hi Riley,

If no one catches the shirt and it falls to the ground, that makes h 0, so:

0= -16t² + 96t + 4

Now, we can solve this using the quadratic formula:

x= [-b +/- sqrt(b²-4ac)]/2a

a= -16

b= 96

c=4

x= [-96 +/- sqrt(96²-4(-16)(4))]/(2(-16))

Now, you will get two answers for x, one when you add the -96 and one when you subtract the negative 96.

x₁= -0.041 seconds

This makes sense as it represents the point in time BEFORE the t-shirt was launched. It's approximately 0.

x₂= 6.04 seconds, the correct answer, the point where the ball completes its parabolic arc and hits the ground.

Answer 2

0 = -16t² + 96t + 4

Can you solve for t and answer? (I would divide both sides by 4).