Question

A 66.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 7.8 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height.

a. What are the interacting objects and how do they interact?

b. Select the height at which the athlete's speed is 7.8 m/s as
* y* = 0. What is her kinetic energy at this point?
What is the gravitational potential energy associated with the
athlete?

c. What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete?

d. Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer.

e. Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.

Answer #1

3. A 67 kg trampolinist leaves the trampoline in the vertical
direction with a velocity of 7 m/s. a) What is the athlete’s
maximum kinetic energy? _________________
b) What is the athlete’s maximum potential gravitational energy?
_________________
c) Plot (on the same graph) the athlete’s potential and kinetic
energy versus time for the entire duration that the athlete is in
the air. On the plot, label the following phases on the graph:
take-off, top of jump, and landing. Also label...

A child is bouncing an a trampoline. The child has a mass of
50.5 kg . She leaves the surface of the trampoline with an initial
upwards velocity of 10.2 m/s . When she reaches height 1.60 m above
the trampoline (still on the way up), she grabs a large
(stationary) plastic block. The mass of the block is 8.00 kg .
(Figure 1)
For this problem, use g=9.80 meters per second per
second for the magnitude of the acceleration...

A 1.90 kg water balloon is shot straight up with an initial
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of the balloon just as it is launched? (b) How
much work does the gravitational force do on the balloon during the
balloon's full ascent? (c) What is the change in
the gravitational potential energy of the balloon–Earth system
during the full ascent? (d) If the gravitational
potential energy is taken to be zero at the launch point,...

A 9.8 kg cannonball was fired from a cannon straight up with an
initial velocity of 42 m/s.
(A) Assuming that all its initial kinetic energy was transformed
into gravitational energy, what is the maximum height that the
cannonball could reach?
(B) Suppose that 20% of its initial kinetic energy was lost due
to friction with the air (air resistance). What is the maximum
height that the cannonball could now reach?
(C) How long will it take, after the cannon...

A 20 kg kid jumps from a moving swing. When she leaves the swing
she is y1=1.0 m above the ground, moving with a speed v1=2 m/s at
an angle 60 degrees above horizontal.
(a) What is the change in potential energy (∆U) as she moves
from the swing to the ground (y =0 m)?
(b) Use conservation of mechanical energy (∆K + ∆U = 0) to find
her speed as she reaches the ground.
(c) What is the change...

A 20 kg kid jumps from a moving swing. When she leaves the swing
she is y1 “ 1.0 m above the ground, moving with a speed v1 “ 2 m{s
at an angle 60 ̋ above horizontal. (a) What is the change in
potential energy (∆U ) as she moves from the swing to the ground (y
“ 0 m)? (2 pts) (b) Use conservation of mechanical energy (∆K ` ∆U
“ 0) to find her speed as she...

A golf ball (m = 50 g) is hit from ground level with an initial
speed of 50 m/s and reaches a maximum height of 25 m. Neglect air
drag.
a. What is the ball’s total mechanical energy just after it has
been hit?
b. What is the ball’s potential energy at the maximum height?
c. What is the ball’s kinetic energy at the maximum height? d.
What is the ball’s speed at the maximum height?

A 41.0-kg skier with an initial speed of 1.5 X 101 m/s coasts up
a 2.50-m-high rise as shown below. The coefficient of friction
between her skis and the snow is 0.0800. a) Where do you define the
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what kind of...

A man of mass m1 = 64.5 kg is skating at v1 = 7.60 m/s behind
his wife of mass m2 = 53.0 kg, who is skating at v2 = 3.80 m/s.
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grabs her around the waist, and they maintain their balance.
(a) Sketch the problem with before-and-after diagrams,
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(b) Is the collision best described as elastic, inelastic, or
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Question 1 (1 point)
Which is not necessary in order to do work on an object (use the
scientific definition of work)?
Question 1 options:
There must be a change in momentum.
A net force must be applied to the object.
The object must undergo a displacement.
A component of the force must be in the direction of motion.
Question 2 (1 point)
The change in gravitational potential energy for a 1.9 kg box
lifted 2.2 m is:
Question 2...

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