# A model rocket is fired vertically upward from rest. Its acceleration for the first 3 seconds is a(t) = 60t at which time the fuel is exhausted and it becomes a freely "falling" body. 14 seconds later, the rocket's parachute opens, and the (down)?

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velocity slows linearly to -18 ft/s in 5 s. The rocket then "floats" to the ground at that rate.

(b) At what time does the rocket reach its maximum height? (Give your answer correct to one decimal place.)

What is that height? (Give your answer correct to the nearest whole number.)

(c) At what time does the rocket land? (Give your answer correct to one decimal place.)

velocity slows linearly to -18 ft/s in 5 s. The rocket then "floats" to the ground at that rate.

(b) At what time does the rocket reach its maximum height? (Give your answer correct to one decimal place.)

What is that height? (Give your answer correct to the nearest whole number.)

(c) At what time does the rocket land? (Give your answer correct to one decimal place.)

##### 1 Answer

Given acceleration

Integrating both sides we obtain

where

Now velocity at

Rewriting (1) in terms of height

To find out the height attained at

At the maximum height

Inserting values we get

Rocket gains maximum height at

To calculate maximum height attained we use the kinematic relation

Maximum height attained is