COLLEGE PHYSICS,VOLUME 1
COLLEGE PHYSICS,VOLUME 1
2nd Edition
ISBN: 9781319115104
Author: Freedman
Publisher: MAC HIGHER
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Chapter 2, Problem 82QAP
To determine

(a)

The maximum altitude of the rocket.

Expert Solution
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Answer to Problem 82QAP

The maximum altitude of the rocket is 1091.7m

Explanation of Solution

Given:

a1 = 2.00 m/s2

a2 = 3.00 m/s2

t1 = 15 sec

t2 = 12 sec

Formula used:

  H=ut+12at2

S = distance travelled

u = initial velocity

a = acceleration

t = time taken

Calculation:

During first stage, the height reached is,

  H1=ut1+12a1t12=0×4+12×2×162=256m

At the end of first stage speed is,

  v1=u+a1t1=0+2×16=32m/s

During second stage, the height reached is,

  H2=v1t2+12a2t22=32×12+12×3×122=600m

At the end of second stage speed is,

  v2=v1+a2t2=32+3×12=68m/s

At the end of second stage, the rocket will be under the effect of gravity, so it will continue to move upwards up to a point where its kinetic energy will be zero.

The time duration for reaching the maximum altitude from the end of second stage is,

  v3=v2gt30=68(9.8×t3)t3=689.8=6.938sec

The distance between the end of second stage and maximum altitude is,

  H3=v2t312gt32=68×6.93812×9.81×(6.938)2=235.7m

So, the maximum height is,

  H1=H1+H2+H3=256+600+235.7=1091.7m

To determine

(b)

The average speed and average velocity when the rocket fall back to launch pad.

Expert Solution
Check Mark

Answer to Problem 82QAP

The average speed is 44.69m/s and average velocity is 0.

Explanation of Solution

Given:

The maximum altitude is 1091.67m

Calculation:

Once rocket reaches the maximum height, it will start to fall and reach the launch pad on Earth surface.

The time duration taken by rocket to fall back is,

  H=v3t4+12×g×t421091.7m=0×t4+12×9.81×t42t4=14.91sec

Total time duration of flight,

  t=t1+t2+t3+t4=15+12+6.938+14.91=48.85sec

Total distance travelled is,

  Ht=H+H=2H=2×1091.7m=2183.4m

So average speed will be,

  S=2183.3448.85=44.69m/s

Since, the initial and final position of rocket is same, so the net displacement is zero. Therefore, the average velocity will be,

  v=Dit=0t=0m/s

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COLLEGE PHYSICS,VOLUME 1

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