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A 200 kg weather rocket is loaded with 100 kg of fuel and
Chapter 2, Problem 49P(choose chapter or problem)
A \(200 \mathrm{~kg}\) weather rocket is loaded with \(100 \mathrm{~kg}\) of fuel and fired straight up. It accelerates upward at \(30 \mathrm{~m} / \mathrm{s}^{2}\) for \(30 \mathrm{~s}\), then runs out of fuel. Ignore any air resistance effects.
a. What is the rocket's maximum altitude?
b. How long is the rocket in the air before hitting the ground?
c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.
Equation Transcription:
Text Transcription:
200 kg
100 kg
30m/s^2
30 s
Questions & Answers
QUESTION:
A \(200 \mathrm{~kg}\) weather rocket is loaded with \(100 \mathrm{~kg}\) of fuel and fired straight up. It accelerates upward at \(30 \mathrm{~m} / \mathrm{s}^{2}\) for \(30 \mathrm{~s}\), then runs out of fuel. Ignore any air resistance effects.
a. What is the rocket's maximum altitude?
b. How long is the rocket in the air before hitting the ground?
c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.
Equation Transcription:
Text Transcription:
200 kg
100 kg
30m/s^2
30 s
ANSWER:
Step 1 of 5
(A)
We are going to find the maximum altitude reached by the weather rocket.
The upward acceleration \(\mathrm{a}_{y}=30 \mathrm{~m} / \mathrm{s}^{2}\)
The time until the fuel runs out \(\mathrm{t}_{1}=30 \mathrm{~s}\)
The initial speed of the rocket \(\mathrm{v}_{\text {is }}=0\)
The acceleration due to gravity \(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\)
The maximum altitude reached by the rocket has two parts. One is until the fuel runs out with \(\mathrm{a}_{y}\) and the other is the motion due to the inertia. The acceleration produced in the second stage is nothing but the acceleration due to gravity \((g)\).