This pod will deal with cannons that fire a shot
that lands on exactly the same level.
The problems bring together the concepts of the pop-up and horizontal
launch problems,
and they are among the most classic physics problems!
Review of vector components
Please answer all questions to 3 significant figures of accuracy.
Basic cannon Problem
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A cannon is aimed at an angle of 30 degrees.
It fires a cannonball with a speed of 20 m/s.
The cannonball rises and falls and then
lands at precisely the vertical level it was fired at.
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First, break the initial velocity
of the cannonball into horizontal and
vertical components using
this method.
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Similarly to a horizontal launch problem,
we will break the motion into two components.
In the horizontal dimension, the object moves at a constant speed forward.
In the vertical dimension, the object is initially moving upward
and then falls downward to the same point, similarly to a
pop-up problem.
Fill out the table below, which describes the quantities involved in this problem:
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Determine the total time that the cannonball is in the air.
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Determine the range of the cannonball, that is, the horizontal displacement
of the cannonball before it strikes the ground.
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We will repeat a similar question with different values.
A cannon is aimed at an angle of 20 degrees.
It fires a cannonball with a speed of 15 m/s.
The cannonball falls to the same vertical position from where it was fired.
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Break the initial velocity of the cannon
into horizontal and vertical components.
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Fill out the table below, which describes the quantities involved.
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Determine the total time that the cannonball is in the air.
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Determine the horizontal range of the cannonball.
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A cannon is aimed at an angle of 85 degrees.
It fires a cannonball with a speed of 40 m/s.
The cannonball falls to the same vertical position from where it was fired.
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Break the initial velocity of the cannon
into horizontal and vertical components.
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Fill out the table below, which describes the quantities involved.
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Determine the total time that the cannonball is in the air.
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Determine the horizontal range of the cannonball.
Use \( g = 9.81 \frac{\text{m}}{\text{s}^2} \)Answer the following questions to three significant figures of accuracy.
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A cannon is at an angle of 45.0 degrees above the horizontal
and fires a shot with an initial velocity of 20.0 m/s.
If the cannonball lands on the same level it was fired at,
determine the horizontal range of the cannonball.
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A cannon is at an angle of 35.0 degrees above the horizontal
and fires a shot with an initial velocity of 28.0 m/s.
If the cannonball lands on the same level it was fired at,
determine the horizontal range of the cannonball.
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A cannon is at an angle of 65.0 degrees above the horizontal
and fires a shot with an initial velocity of 10.0 m/s.
If the cannonball lands on the same level it was fired at,
determine the horizontal range of the cannonball.
Answers: