Question

10. The height, h, in meters aboveground, of a projectile at any time, t, in seconds, after the launch is defined by the function h(t) = −6t2 + 15t + 2. The graph of this function is shown below. When rounded to the nearest tenth, what is the maximum height reached by the projectile, how long did it take to reach its maximum height, and from what height was the projectile initially launched?

A. The projectile reached a maximum height of 15.0 meters in 2.0 seconds and it was launched from 1.0 meter above the ground.

B. The projectile reached a maximum height of 11.4 meters in 1.3 seconds and it was launched from 2.0 meters above the ground.

C. The projectile reached a maximum height of 11.2 meters in 1.2 seconds and it was launched from 2.1 meters above the ground.

D. The projectile reached a maximum height of 2.0 meters in 1.2 seconds and it was launched from 11.9 meters above the ground.

Answer 1

Answer:

Option B

The projectile reached a maximum height of 11.4 meters in 1.3 seconds and it was launched from 2.0 meters above the ground.

Step-by-step explanation:

$h(t) = −6t^{2} + 15t + 2$

Differentiating the above equation with respect to time t

h'=-12t+15

h'=0

12t=15

$t=\frac {15}{12}=1.25 s$

$h_{max}= −6t^{2} + 15t + 2= −6\times 1.25^{2} + 15\times 1.25 + 2=11.375 m\approx 11.4 m$

at t=0 then $h=−6\times 0^{2} + 15\times 0 + 2=2 m$