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One-Dimensional Kinematics: Speed and Velocity

by Soaring Crane
Tags: kinematics, onedimensional, speed, velocity
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Soaring Crane
#1
Sep5-06, 05:52 PM
P: 484
A woman stands at the edge of a cliff, holding one ball in each hand. At time t_0, she throws one ball straight up with speed v_0 and the other straight down, also with speed v_0. For the following questions neglect air resistance.

A. If the ball that is thrown downward has an acceleration of magnitude a at the instant of its release (i.e., when there is no longer any force on the ball due to the woman's hand), what is the relationship between a and g, the magnitude of the acceleration of gravity?

a. a > g
b. a = g
c. a < g
Doesn't the ball have a constant downward acceleration of 9.80 m/s^2?


B. Which ball has the greater acceleration at the instant of release?

a. the ball thrown upward
b. the ball thrown downward
c. Neither; the accelerations of both balls are the same.


C. Which ball has the greater speed at the instant of release?

a. the ball thrown upward
b. the ball thrown downward
c. Neither; the speeds are the same.
Both balls have the same givin initial speed v_0, so the speeds are the same?

D. Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that time)?

a. the ball thrown upward
b. the ball thrown downward
c. Neither; the average speeds of both balls are the same.
The ball thrown downward has a greater average speed because it speeds up due to gravity?


E. Which ball hits the ground with greater speed?

a. the ball thrown upward
b. the ball thrown downward
c. Neither; the balls hit the ground with the same speed.
Don't both balls have a final velocity of 0 m/s if they hit the ground?

Thank you for any replies.
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berkeman
#2
Sep5-06, 05:59 PM
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I believe you got all the right answers, but your reason on the last one is hopefully a typo. The balls do not hit the ground at 0 m/s, they have some velocity. The tricky reason that they are equal is that the ball thrown upward has V_0 as it starts up and again as it comes down past the same height, which then matches the intial start condition (velocity and direction) of the 2nd ball.

Makes sense?
Saketh
#3
Sep5-06, 06:04 PM
P: 262
Don't both balls have a final velocity of 0 m/s if they hit the ground?
I used to think that too, which messed up my whole mental perception of projectile motion for a while.

The speed with which the objects hit the ground is not the same as the speed that the objects have after hitting the ground. If you drop a ball from a height of 10m, it won't hit the ground with a speed of 0 m/s. It will accelerate and hit the ground with a certain velocity.


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