Question

Stefanie is in a freestyle aerial competition. The equation

h = - 16t + 30t +10 models Stefanie's height h, in
feet, t in seconds after leaving the ramp.
a. How long is Stefanie in the air?
B. When will Stefanien reach a height of 15 feet?

Answer 1

A = about 2.2 seconds

B = between 0.2 and 1.7 seconds

Explanation:

A .to calculate the time in the air, we have to replache h=0.

h = - 16t + 30t +10

0 = - 16t + 30t +10

For: ax2+ bx + c

x =[ -b ± √b²-4ac] /2a

a=-16 ; b=30 ; c=10

Replacing with the values given:

x =[ -30 ± √(30)²-4(-16)10] /2(-16)

x = [ -30 ± √900 +640] /-32

x = [ -30 ± √1,540] /-32

x = [-30 ± 39.24] /-32

Negative:

x = [-30 -39.24] /-32 = 2.16 seconds = about 2.2 seconds

B. .to calculate this, we have to replache h=15.

15 = - 16t + 30t +10

0 = - 16t + 30t +10-15

0= - 16t + 30t -5

a=-16 ; b=30 ; c=-5

Applying the quadratic formula again:

x =[ -30 ± √(30)²-4(-16)-5] /2(-16)

x = [ -30 ± √900-320] /-32

x = [ -30 ± √580] /-32

x = [-30 ± 24.08] /-32

Positive:

x = [-30 +24.08] /-32 = 0.18 seconds =0.2 seconds

Negative:

x = [-30 -24.08] /-32 = 1.7seconds

Feel free to ask for more if needed or if you did not understand something.