A 3600 kg rocket traveling at 2900 m/s is moving freely through space on a journey to the moon. The ground controllers find that the rocket has drifted off course and that it must change direction by 11◦ if it is to hit the moon. By radio control the rocket's engines are fired instantaneously (i. e., as a single pellet) in a direction perpendicular to that of the rocket's motion. The gases are expelled (i. e., the pellet) at a speed of 4300 m/s (relative to the rocket). What mass of gas must be expelled to make the needed course correction? Answer in units of kg.

Question

Physics

Aleah Pierce

25 December, 03:49

A 3600 kg rocket traveling at 2900 m/s is moving freely through space on a journey to the moon. The ground controllers find that the rocket has drifted off course and that it must change direction by 11◦ if it is to hit the moon. By radio control the rocket's engines are fired instantaneously (i. e., as a single pellet) in a direction perpendicular to that of the rocket's motion. The gases are expelled (i. e., the pellet) at a speed of 4300 m/s (relative to the rocket). What mass of gas must be expelled to make the needed course correction? Answer in units of kg.

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Answers (1)

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Dunlap · Answer 1

m=417.24 kg

Explanation:

Given Data

Initial mass of rocket M = 3600 Kg

Initial velocity of rocket vi = 2900 m/s

velocity of gas vg = 4300 m/s

Θ = 11° angle in degrees

To find

m = mass of gas

Solution

Let m = mass of gas

first to find Initial speed with angle given

So

Vi=vi*tanΘ ... tan angle

Vi = 2900m/s * tan (11°)

Vi=563.7 m/s

Now to find mass

m = (M * vi * tanΘ) / (vg + vi tanΘ)

put the values as we have already solve vi * tanΘ

m = (3600 kg * 563.7m/s) / (4300 m/s + 563.7 m/s)

m=417.24 kg