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kondaur [170]
3 years ago
11

A cyclist is traveling at 10m/s when he comes to a hill. He stops pedaling at the bottom of the hill and lets the bicycle coast

up the hill. Assuming no energy is lost to friction and ???? equals 10m/s2 , what will be the vertical height of the bicycle when it stops coasting?
Physics
1 answer:
Novay_Z [31]3 years ago
4 0

Answer:

Vertical height = 5 m

Explanation:

Given:

There is no frictional losses. So, energy is conserved.

Acceleration due to gravity (g) = 10 m/s²

Initial velocity at the bottom of hill (u) = 10 m/s

Final velocity at the moment it stops on the hill (v) = 0 m/s

Initial height at the bottom (h₁) = 0 m

Final height (h₂) = ?

As there are no frictional losses, the total energy remains conserved.

So, increase in potential energy is equal to decrease in kinetic energy.

Increase in potential energy is given as:

\Delta U=mg(h_2-h_1)=10mh_2

Decrease in kinetic energy is given as:

\Delta KE=\frac{1}{2}m(u^2-v^2)=\frac{1}{2}m(10^2)=50m

Now, \Delta U =\Delta KE

⇒ 10mh_2=50m

⇒ h_2=\frac{50}{10}=5\ m

Therefore, the vertical height of the bicycle when it stops coasting is 5 m.

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A student at a window on the second floor of a dorm sees her physics professor walking on the sidewalk beside the building. she
klasskru [66]
Refer to the diagram shown below.

In order for the balloon to strike the professor's head, th balloon should drop by 18 - 1.7 = 16.3 m in the time at the professor takes to walk 1 m.
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t = (1 m)/(0.45 m/s) = 2.2222 s

The initial vertical velocity of the balloon is zero.
The vertical drop of the balloon in 2.2222 s is
h = (1/2)*(9.8 m/s²)*(2.2222 s)² = 24.197 m

Because 24.97 > 16.3, the balloon lands in front of the professor, and does not hit the professor.

The time for the balloon to hit the ground is
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t = 1.9166 s

The time difference is 2.2222 - 1.9166 = 0.3056 s
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Answer: 
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