Question

Alegbra 2: pls help!!

Kiara and Sean are setting off model rockets. Kiara's rocket's flight pattern can be modeled by the function f(t)= -16t² +80t. Sean's rocket's flight
pattern can be modeled by the function h(t) = -16t² + 120t+64. In each function, t is the time in seconds after the rockets launch and f(t) and h(t)
are the heights of the rockets in feet.
How many seconds after Kiara's rocket returns to the ground does
Sean's rocket return to the ground?
Enter your response as a numeric answer. Do not include spaces, units,
or commas in your response.

Answer 1

Sean's rocket lands 3 seconds after Kiara's rocket.

Explanation:

Kiara: f(t)= -16t² + 80t

Sean: h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time. We need to be suspicious of Sean's rocket launch. His equation for height has "+64" at the end, whereas Kiara's has no such term. The +64 is the starting height iof Sean's rocket. So Kiara has a 64 foot disadvantage from the start. But if it is a race to the ground, then the 64 feet may be a disadvantage. [Turn the rocket upside down, in that case. :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground). So we can set both equation to 0 and calculate t:

Kiara: f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring. I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5. Kiara's rocket lands in 5 seconds.

Sean: h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds. Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.