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A 500 g model rocket is resting horizontally at the top
Chapter 8, Problem 27P(choose chapter or problem)
Problem 27P
A 500 g model rocket is resting horizontally at the top edge of a 40-m-high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of 0.5 m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant 20 N horizontal thrust away from the wall.
a. How far from the base of the wall does the rocket land?
b. Describe the trajectory of the rocket while it travels to the ground.
Questions & Answers
QUESTION:
Problem 27P
A 500 g model rocket is resting horizontally at the top edge of a 40-m-high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of 0.5 m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant 20 N horizontal thrust away from the wall.
a. How far from the base of the wall does the rocket land?
b. Describe the trajectory of the rocket while it travels to the ground.
ANSWER:
Step 1 of 2
Part a
We are required to calculate the distance from the wall where the rocket lands. The vertical height of the wall is \(40.0 \mathrm{~m}\).
Therefore, \(40.0=\frac{1}{2} g t^{2}\)
\(t^{2}=80 / 9.8 \mathrm{~s}^{2}\)
\(t=2.86 \mathrm{~s}\)
For horizontal motion, The force is \(20 \mathrm{~N}\) and the mass of the model rocket is \(500 \mathrm{~g}\) or \(0.5 \mathrm{~kg}\).
Therefore, the acceleration of the model rocket along the horizontal path moved is,
\(=20 / 0.5 \mathrm{~m} / \mathrm{s}^{2}=40 \mathrm{~m} / \mathrm{s}^{2}\)
Therefore, the horizontal distance moved by the model rocket is,
\(=0.5 \times 2.86+\frac{1}{2} \times 40 \times(2.86)^{2} \mathrm{~m}\)
\(=165 \mathrm{~m}\)
The rocket moves to a distance of \(165 \mathrm{~m}\) from the base of the wall.