Concept explainers
A spring cannon is located at the edge of a table that is 1.20 m above the floor. A steel ball is launched from the cannon with speed vi at 35.0° above the horizontal. (a) Find the horizontal position of the ball as a function of vi at the instant it lands on the floor. We write this function as x(vi). Evaluate x for (b) vi = 0.100 m/s and for (c) vi = 100 m/s. (d) Assume vi is close to but not equal to zero. Show that one term in the answer to part (a) dominates so that the function x(vi) reduces to a simpler form. (c) If vi is very large, what is the approximate form of x(v)? (f) Describe the overall shape of the graph of the function x(vi).
(a)
The horizontal position of the ball as a function of
Answer to Problem 73AP
The horizontal position of the ball as a function of
Explanation of Solution
Given info: The located at the spring cannon is
Formula to calculate the vertical distance covered by the ball is,
Here,
The vertical component of the velocity is,
Here,
Substitute
Substitute
Solve the equation (2).
Formula to calculate the horizontal distance covered by the ball is,
Here,
The horizontal component of the velocity is,
Substitute
Substitute
Conclusion:
Therefore, the horizontal position of the ball as a function of
(b)
The horizontal position of the ball as
Answer to Problem 73AP
The horizontal position the ball as
Explanation of Solution
Given info: The located at the spring cannon is
From equation (IV),
Substitute
Conclusion:
Therefore, the horizontal position the ball as
(c)
The horizontal position of the ball as
Answer to Problem 73AP
The horizontal position the ball as
Explanation of Solution
Given info: The located at the spring cannon is
From equation (4),
Substitute
Conclusion:
Therefore, the horizontal position the ball as
(d)
The horizontal position of the ball as a function of
Answer to Problem 73AP
The horizontal position of the ball as a function of
Explanation of Solution
Given info: The located at the spring cannon is
From equation (IV),
The value of
Substitute
Conclusion:
Therefore, the horizontal position of the ball as a function of
(e)
The horizontal position of the ball as a function of
Answer to Problem 73AP
The horizontal position of the ball as a function of
Explanation of Solution
Given info: The located at the spring cannon is
From equation (4),
The term is
Conclusion:
Therefore, the horizontal position of the ball as a function of
(f)
The overall shape of the graph of the function
Answer to Problem 73AP
In starting condition graph
Explanation of Solution
Given info: The located at the spring cannon is
The graph of
Conclusion:
Therefore, the starting condition graph
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Chapter 4 Solutions
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