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Physics / College Physics 1 / Chapter 4 / Problem 45

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

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Integrated Concepts A large rocket has a mass of 2.00×106

Chapter 4, Problem 45

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QUESTION:

Problem 45PE

Integrated Concepts A large rocket has a mass of 2.00×106 kg at takeoff, and its engines produce a thrust of 3.50×107 N . (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust? (c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

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QUESTION:

Problem 45PE

Integrated Concepts A large rocket has a mass of 2.00×106 kg at takeoff, and its engines produce a thrust of 3.50×107 N . (a) Find its initial acceleration if it takes off vertically. (b) How long does it take to reach a velocity of 120 km/h straight up, assuming constant mass and thrust? (c) In reality, the mass of a rocket decreases significantly as its fuel is consumed. Describe qualitatively how this affects the acceleration and time for this motion.

ANSWER:

Solution 45PE

We are required to calculate the acceleration of the rocket’s vertical motion. We are also required to calculate the time the rocket would need to attain the given final velocity.

Part a

Step 1 of 3

The rocket takes off vertically. Therefore, the net force on it would be

$F{\ }_{net}=Thrust-Weight$

$Mass\times{}a{\ }_{net}=3.50\times{}1{0}^{7}$ N $-mass\times{}g$

$2.00\times{}1{0}^{6}$ kg $\times{}a{\ }_{net}=3.50\times{}1{0}^{7}$ N $-2.00\times{}1{0}^{6}$ kg $\times{}9.8$ m/s2

$a{\ }_{net}=\frac{3.50}{2.00}\times{}10\$ m/s2 $-$ 9.8 m/s2

$a{\ }_{net}=7.70$ m/s2

Therefore, the initial acceleration of the rocket is 7.70 m/s2.

Part b

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