Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 3, Problem 9P
(a)
To determine
To Find: The way the velocity vector related geometrically to the path of the particle.
(b)
To determine
To Draw: The velocity vector of the particle on the curved path.
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A projectile is shot from ground level at 100 ft/s at a launch angle of θ that is between θ and π /2. Assume that the projectile is acted on by gravity, but not air resistance. Then, in a simple projectile-motion model it can be shown that the projectile lands at a distance R(θ) = 625 sinθcosθ ft from the launch point. What is the rate of change of the range with respect to the launch angle? For what angles does the range increase/decrease with increasing launch angle? What angle provides the maximum range, and what is that maximum range?
You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity
v
at an angle ? with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 8.60 m/s, and the initial vertical velocity be 12.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released.
(a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height.
maximum height above ground
m
time to reach maximum height
s
(b) Repeat your calculations choosing the origin at the base of the building.
maximum height above ground
m
time to reach maximum height
s
Sketch the vectors representing the projectile’s horizontal and vertical velocities. Note that the length of the directed line segment must be proportional to the vector’s magnitude and the arrowhead must point to the vector’s direction.
Chapter 3 Solutions
Physics for Scientists and Engineers
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