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Shooting the Breeze

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Please see attached for actual problem. Note that I only need help with the last part of this problem!

PSS 6.1: Shooting the Breeze
Learning Goal: To practice Problem-Solving Strategy 6.1 for projectile motion problems.
A student throws rocks from the roof of a building. All of the rocks are thrown with the same initial speed and from the same initial height , but they are thrown with different angles with respect to the horizontal. Derive an expression for the minimum angle that the landing velocity of the rock can make with the horizontal.
MODEL: Make simplifying assumptions.
VISUALIZE: Use a pictorial representation. Establish a coordinate system with the x axis horizontal and the y axis vertical. Show important points in the motion on a sketch. Define symbols and identify what you are trying to find.
SOLVE: The acceleration is known: and . Thus the problem becomes one of kinematics. The kinematic equations are

,
where is the same for the horizontal and vertical conponents of the motion. Find from one component, then use that value for the other component.
ASSESS: Check that your result has the correct units, is reasonable, and answers the question.
Model
Start by making simplifying assumptions.
A. Which of the following assumptions should you make about the rock?
The rock should be treated as a small particle.
The rock should be treated as a thin weightless rope shaped like the rock's trajectory.
B. Which of the following assumptions should you make about the air resistance acting on the rock?
It decreases as the rock falls.
It increases as the rock falls.
It is negligible.

C. Which of the following assumptions should you make about the acceleration of the rock?
It decreases as the rock falls.
It increase as the rock falls.
It is negligible.
It is nonzero and constant.
It depends on the launch angle.
Visualize
Now draw a pictorial sketch including all the elements listed in the problem-solving strategy. Use your sketch to answer the following questions.
A. As stated in the strategy, your coordinate system should have the x axis horizontal and the y axis vertical. Where is the best place to put the origin?
At ground level below the point where the rock is released
At the peak of the trajectory
At ground level below the peak of the trajectory
At the point where the rock is released
At the point where the rock strikes the ground

B. The problem asks about the minimum angle at which the rock can strike the ground. If you sketched a good selection of trajectories, your diagram should help you see what determines this angle. To achieve the minimum final angle, at what initial angle (measured relative to the x axis) must you throw the rock?

Enter the angle in degrees. A rock thrown straight up has ; a rock thrown straight down has ; a rock thrown horizontally has . If the final angle does not depend only on the initial angle, type NA.
=
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Because the direction of final angle depends on the final velocity components in horizontal and vertical directions. and inturn the initial direction of projection.

For the final minimum angle, the vertical component of the final velocity should ...

Solution Summary

The solution provides a step-by-step calculation for the minimum final angle at which a falling rock can strike the ground when it has been thrown off a building.

$2.19