Arocket is launched into the air. the projectile motion of the rocket can be modeled using  h(t)  =  112t  –16t2, where  tis 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? after 2.0 secondsafter 3.5 secondsafter 4.5 secondsafter 7.0 seconds

B after 3.5 seconds

Step-by-step explanation:

set h(t) = 196, that is

112t - 16t² = 196 ( rearrange into standard form )

-16t² + 112t - 196 = 0 ← in standard form

divide through by - 4

4t² - 28t + 49 = 0

(2t - 7)² = 0 ← factor as a perfect square

2t - 7 = 0 ⇒ t = = 3.5

The rocket is at 196 feet after 3.5 seconds

after 3.5 seconds

Step-by-step explanation:

Given : The projectile motion of the rocket can be modeled using

To Find : When will the rocket be 196 feet in the air?

Solution:

Expression:

Hence the rocket will be at height 196 feet in the air after 3.5 seconds .

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