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Chapter 2: Q. 56 (page 62)

A 1000 kg weather rocket is launched straight up. The rocket

motor provides a constant acceleration for 16 s, then the motor stops. The rocket altitude 20 s after launch is 5100 m. You can ignore any effects of air resistance. What was the rocket鈥檚 acceleration during the first 16 s?

Short Answer

Expert verified

The rocket's acceleration during the first16sis29.97m/s2.

Step by step solution

01

Given data

Time of rocket motion, t=16s.

The rocket altitude after timet'=20s is, s=5100m.

We have to find the acceleration of the rocket.

02

Determination of displacement of the rocket in 16 s

Speed of the rocket after 16s,

v=u+atv=0+16av=16a...1

Displacement of the rocket in 16s,

s=ut+12at2s=0+12at2s=12at2...2

03

Determination of displacement of the rocket  after 16 s

After moving for 16s,the motor of the rocket stops and its altitude after 20-16s=4sbecomes 5100m.

So the displacement of the rocket after 16sis,

role="math" localid="1648488020296" x=vt+12gt2x=16a脳4-12脳9.8脳42x=64a-78.4...3

04

Determination of the acceleration

According to the question, the altitude of the rocket after 16sis, x+s=5100

Thus from equation 2,3, we can write,

role="math" localid="1648488126578" 5100=12a脳162+64a-78.45100=128a+64a-78.4192a=5100+78.4a=5178.4192a=29.97m/s2

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