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course Phy 241
08/06 6:00 pm
Question: `q001. Note that this assignment contains 5 questions.
How long does it take for an object dropped from rest to fall 2 meters under the influence of gravity?
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Your solution:
v0 = 0 m/s, ds = 2 m, a = 9.8 m/s^2
ds = v0dt +.5adt^2
ds = .5adt^2
ds/.5a =.5adt^2/.5a
sqrt(ds/.5a) = sqrt(dt^2)
sqrt(ds/.5a) = dt
sqrt(2 m/(.5(9.8 m/s)) = dt
sqrt(.4081 s^2) = dt
.638 s = dt
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Question: `q002. While an object dropped from rest falls 2 meters under the influence of gravity, another object moves along a level surface at 12 meters/second. How far does the second object move during the time required for the first object to fall?
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Your solution:
ds = 2 m, delta = 12 m/sec
ds = vAve * dt
ds = 12 m/sec * 64 sec
ds = 8 meters
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Question: `q003. An object rolls off the edge of a tabletop and falls to the floor. At the instant it leaves the edge of the table is moving at 6 meters/second, and the distance from the tabletop to the floor is 1.5 meters.
Since if we neglect air resistance there is zero net force in the horizontal direction, the horizontal velocity of the object will remain unchanged.
Since the gravitational force acts in the vertical direction, motion in the vertical direction will undergo the acceleration of gravity. Since at the instant the object leaves the tabletop its motion is entirely in the horizontal direction, the vertical motion will also be characterized by an initial velocity of zero.
How far will the object therefore travel in the horizontal direction before it strikes the floor?
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Your solution:
ds = v0dt + .5adt^2
ds = .5adt^2
ds/.5a = .5adt^2/.5a
sqrt(ds/.5a) = sqrt(dt^2)
sqrt(ds/.5a) = dt
sqrt(1.5 m/(.5(9.8 m/s^2)) = dt
sqrt(.3 s^2) = dt
.547 sec = dt
ds horizontal = 6 m/s * .547 s
ds horizontal = 3.28 m
confidence rating #$&*:
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Question: `q004. An object whose initial velocity is in the horizontal direction descends through a distance of 4 meters before it strikes the ground. It travels 32 meters in the horizontal direction during this time. What was its initial horizontal velocity? What are its horizontal and vertical velocities at the instant of its first contact with the ground?
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Your solution:
sqrt(ds/.5a) = dt
sqrt(4 m/.5(9.8 m/s^2)) = dt
sqrt(.81 s^2) = dt
.9 = dt
Ave horizontal velocity
32 m/(.9 sec)
= 35 m/s
confidence rating #$&*:
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If you understand the assignment and were able to solve the previously given problems from your worksheets, you should be able to complete most of the following problems quickly and easily. If you experience difficulty with some of these problems, you will be given notes and we will work to resolve difficulties.
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Question: `q005. An object falls from rest from a height of 10 meters, at the same time moving in the horizontal direction at 4 meters / second.
How far does it travel in the horizontal direction before striking the level ground below?
What are its horizontal and vertical velocities, and its speed, at the instant it first encounters the ground?
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Your solution:
sqrt(ds/.5a) = dt
sqrt(10 m/(.5(9.8 m/s^2)) = dt
sqrt(2.04 s^2) = dt
1.43 sec = dt
ds = 4 m/sec * 1.43 sec
ds = 5.72 m
Horizontal velocity
10 m * 1.43 sec
= 14.3 m/sec
Speed
v =5.72 m / 1.43 sec
v = 4 m/sec
Vertical velocity
0 m/s
@&
His speed is the magnitude of the velocity vector.
You have the components of the velocity vector, so you can find its magnitude.
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confidence rating #$&*:
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&#Good responses. See my notes and let me know if you have questions. &#