Question

A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the time since launch in seconds and h(t) is the height of the rocket at time t. When will the rocket be 196 feet in the air?
 
A.) after 2.0 seconds

B.) after 3.5 seconds

C.) after 4.5 seconds

D.) after 7.0 seconds

*The answer is B, after 3.5 seconds. If anyone wants to properly explain how this is the correct answer, I will give you brainliest.*

Answer 1

.

h ( t ) = 112 t - 16 t²
When the rocket is 196 feet in the air:
196 = 112 t - 16 t²
16 t² - 112 t + 196 = 0

divide everything by 4 ( just makes numbers smaller and easier to work with)

4 t² - 28 t + 49 = 0

Now factor the equation:
( 2 t - 7 )² = 0
2 t - 7 = 0
2 t = 7
t = 7 : 2
t = 3.5 s

The rocket will be 196 feet in the air after 3.5 seconds.

Answer 2

Answer:

The Answer is B.) after 3.5 seconds

Step-by-step explanation:

i just got a 100 on the quiz