Kehlani launches a toy rocket from a platform. The height of the rocket in feet is given by h= -16t^2 + 72t + 144 where t represents the time in seconds after launch. How long is the rocket in the air?

To find how long the rocket is in the air, we need to find the time when the rocket reaches its maximum height. To do this, we can take the derivative of the height equation to find the rocket's velocity, then set the velocity equal to zero and solve for t.

The derivative of the height equation is: dh/dt = -32t + 72

Setting this equal to zero and solving for t gives us: 0 = -32t + 72

32t = 72

t = 2.25 seconds

This is the time when the rocket reaches its maximum height. Since the rocket is launched at time t=0, it is in the air for 2.25 seconds.

mhanifa mhanifa · Answer 2 · 2022-12-10T16:59:15+01:00

mhanifa mhanifa

10-12-2022

Answer:

6 seconds

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Rocket is in the air until it hits the ground.

Therefore we need to find the value of t when h = 0.

- 16t² + 72t + 144 = 0
2t² - 9t - 18 = 0
2t² - 12t + 3t - 18 = 0
2t(t - 6) + 3(t - 6) = 0
(t - 6)(2t + 3) = 0
t - 6 = 0 or 2t + 3 = 0
t = 6 or t = - 3/2 (discarded as negative)

The rocket is in the air for 6 seconds.

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