A model rocket is launched with an initial velocity of 200 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by . How many seconds after the launch will the rocket be 100 ft above the ground? Round to the nearest hundredth of a second.
A) 0.26 s and 12.24 s
B) 0.52 s and 11.98 s
C) 23.96 s
D) 0.48 s and 12.98 s
E) 1.04 s and 23.96 s

Question

A model rocket is launched with an initial velocity of 200 ft/s. The height, h, in feet, of the rocket t seconds after the launch is given by  . How many seconds after the launch will the rocket be 100 ft above the ground? Round to the nearest hundredth of a second.
A) 0.26 s and 12.24 s 
B) 0.52 s and 11.98 s 
C) 23.96 s 
D) 0.48 s and 12.98 s 
E) 1.04 s and 23.96 s

Quizplus · Accepted Answer

We need to find the time at which the height of the rocket is 100 ft.

Setting $h$ equal to 100 and solving for $t$, we get:

$$100 = -16t^2 + 200t + 160$$
$$0 = -8t^2 + 20t + 8$$
$$0 = -t^2 + \frac{5}{2}t + 1$$
$$0 = \left( -t + 1 \right) \left( t + 1 \right)$$

The solutions are $t = 1$ and $t = -1.5$. Since the time must be positive, we reject $t=-1.5$ and conclude that the rocket will be 100 ft above the ground 1 second after the launch.

The only answer choice that includes 1 second as a possible solution is B: 0.52 s and 11.98 s. Testing this answer, we can see that the rocket indeed reaches a height of 100 ft around 1 second after launch.

A Model Rocket Is Launched with an Initial Velocity of 200