An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
An exercise program. A 75 kg person is put on an exercise program by a physical therapist, the goal being to burn up 500 food calories in each daily session. Recall that human muscles are about 20% efficient in converting the energy they use up into mechanical energy. The exercise program consists of a set of consecutive high jumps, each one 50 cm into the air (which is pretty good for a human) and lasting 2.0 s, on the average. How many jumps should the person do per session, and how much time should be set aside for each session? Do you think that this is a physically reasonable exercise session?
A 2 kg ball is thrown off a 73 m high cliff with a speed of 4 m/s. How fast (in m/s) is the ball going when it hits the ground?
Use g = 9.8 m/s2.
We are now able to define a mathematical formula for gravitational potential energy.
Near the Earth's surface, the gravitational potential energy of a system consisting of the earth and an object with a mass m is
EP = mgh,
where g is the acceleration of gravity (9.80 m/s2) and h is the height above ground level (positive upward).
Note that the "ground level" could really be any height we choose, because what's really important is the change in potential energy. The difference between two heights always gives the same change in potential energy, regardless of where we set the "zero" of height. In other words, if we find the change in potential energy
ΔEP = EP,f − EP,i,
the final potential energy minus the initial, we have
ΔEP = mghf − mghi = mgΔh.
The change in gravitational potential energy is just mg times the change in height.
Let's return to our ball-Earth example, only now let's examine a case where a ball is rising in the air.
You toss a ball with a mass of 0.703 kg upward.…
Question 3.
Siblings Alice and Bob saved their money all summer to buy a water balloon launcher, and they are eager
to take it for a test run. Younger brother Bob thinks he's a pretty fast runner with a top speed of 5 m/s.
Не
poses
the following challenge to his sister: "I'll stand 20 m from you and I'll start running away as soon
as you launch a water balloon. See if you can hit me!" Unfortunately for Bob, Alice is a physics 8A ace and
knows exactly what needs to be done to soak her brother.
(a) Set the origin of your coordinate system at Alice's position with Bob starting along the positive x-axis
(and running along the x-axis). Assuming Bob runs at a constant velocity, what is Bob's trajectory
rB(t)?
(b) Suppose the water balloon launcher is limited to only firing at an angle of T/4. In terms of the unknown
initial launch speed v, what is the trajectory of the water balloon rwB(t)?
(c) What speed v should Alice launch with to ensure a direct hit?
(d) How long does the balloon take…
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