## Hovercraft B/C

Birdmusic
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### Hovercraft B/C

No hovercraft question marathon yet? I think I'll start one.

A train has an initial velocity of 4 m/s. It speeds up with constant acceleration to 8 m/s over a period of 2 seconds. What is its displacement? What equation did you use?
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heyimben
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...

Zioly
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### Re: Hovercraft B/C

I used delta(x)=v(initial)t+1/2at^2, one of the kinematic equations.

I also got 24 meters.
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Froggie
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### Re: Hovercraft B/C

Make sure to use the “HIDE” thing next time.
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Birdmusic
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...
Correct! Since you answered first, you get to post the next question!
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heyimben
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...
Correct! Since you answered first, you get to post the next question!
If a person were walking at the average speed of 2.5 mph from District 12 to District 13 and it takes a week to get there, how fast is the hovercraft traveling from District 12 to District 13, which makes it there in 45 min?

WhatScience?
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...
Correct! Since you answered first, you get to post the next question!
If a person were walking at the average speed of 2.5 mph from District 12 to District 13 and it takes a week to get there, how fast is the hovercraft traveling from District 12 to District 13, which makes it there in 45 min?
heyimben....how much of that time is gone to sleep?
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Justin72835
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...
Correct! Since you answered first, you get to post the next question!
If a person were walking at the average speed of 2.5 mph from District 12 to District 13 and it takes a week to get there, how fast is the hovercraft traveling from District 12 to District 13, which makes it there in 45 min?
You can assume that the person is walking nonstop (without taking rest) because he uses the term "average speed".

One week is equivalent to 168 hours. If the person walks at a speed of 2.5 mph for 168 hours, then the distance between the two points is 420 miles. To find the average speed of the hovercraft, use the formula distance/time, or in this case 420 miles/0.75 hours = 560 mph.

Next question: You have a solid cube of mass 'm' which is attached to a nearby wall using a massless, ideal spring of constant 'k'. If you launch an arrow of velocity 'v' and mass 'M' directly at the solid cube, what is the maximum compression of the spring if:

1) the arrow sticks into the solid after hitting it?

2) the arrow bounces off of the cube perfectly elastically?
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SciolyMaster
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### Re: Hovercraft B/C

24m? I literally just found a basic formula for displacement...
That is incorrect. 8 m/s^2 is what the train accelerates TO from the initial velocity of 4 m/s^2, not the acceleration itself, which would be (8-4)/2 = 2. Therefore, d = vi*t + 0.5*a*t^2 = 4*2 + 0.5*2*2^2 = 12, so the correct answer is 12 meters.
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### Re: Hovercraft B/C

Next question: You have a solid cube of mass 'm' which is attached to a nearby wall using a massless, ideal spring of constant 'k'. If you launch an arrow of velocity 'v' and mass 'M' directly at the solid cube, what is the maximum compression of the spring if:

1) the arrow sticks into the solid after hitting it?

2) the arrow bounces off of the cube perfectly elastically?

Justin72835
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### Re: Hovercraft B/C

Next question: You have a solid cube of mass 'm' which is attached to a nearby wall using a massless, ideal spring of constant 'k'. If you launch an arrow of velocity 'v' and mass 'M' directly at the solid cube, what is the maximum compression of the spring if:

1) the arrow sticks into the solid after hitting it?

2) the arrow bounces off of the cube perfectly elastically?
You're definitely on the right track (I see that you already found the final velocities of the objects after the collision). Using the final velocity, you can find the kinetic energy of the object after the collision and set it equal to 1/2kx^2 and solve for x. This works because maximum compression occurs when the objects kinetic energy has been converted completely into potential energy.
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Justin72835
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### Re: Hovercraft B/C

Since nobody is going:

You have a very long ramp with an inclination of 35 degrees. You give a hollow sphere a translational velocity of 23 m/s toward the base of the ramp. The sphere has a mass of 4 kg and a radius of 0.25 m.

a) What is the hollow sphere's total kinetic energy before rolling up the ramp?

b) To what height above the ground will the sphere roll up the ramp before rolling back down? Assume that it rolls without slipping.
"The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings."

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Riptide
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### Re: Hovercraft B/C

Since nobody is going:

You have a very long ramp with an inclination of 35 degrees. You give a hollow sphere a translational velocity of 23 m/s toward the base of the ramp. The sphere has a mass of 4 kg and a radius of 0.25 m.

a) What is the hollow sphere's total kinetic energy before rolling up the ramp?

b) To what height above the ground will the sphere roll up the ramp before rolling back down? Assume that it rolls without slipping.
Last edited by Riptide on January 10th, 2018, 7:18 pm, edited 1 time in total.
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Justin72835
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### Re: Hovercraft B/C

Since nobody is going:

You have a very long ramp with an inclination of 35 degrees. You give a hollow sphere a translational velocity of 23 m/s toward the base of the ramp. The sphere has a mass of 4 kg and a radius of 0.25 m.

a) What is the hollow sphere's total kinetic energy before rolling up the ramp?

b) To what height above the ground will the sphere roll up the ramp before rolling back down? Assume that it rolls without slipping.
Hey, great job! Now its your turn.
Last edited by Justin72835 on January 10th, 2018, 7:37 pm, edited 1 time in total.
"The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings."

University of Texas at Austin '23
Seven Lakes High School '19

Justin72835
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Posts: 175
Joined: June 25th, 2017, 7:06 am
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### Re: Hovercraft B/C

Since nobody is going:

You have a very long ramp with an inclination of 35 degrees. You give a hollow sphere a translational velocity of 23 m/s toward the base of the ramp. The sphere has a mass of 4 kg and a radius of 0.25 m.

a) What is the hollow sphere's total kinetic energy before rolling up the ramp?

b) To what height above the ground will the sphere roll up the ramp before rolling back down? Assume that it rolls without slipping.
Cool shortcut?
"The fault, dear Brutus, is not in our stars,
But in ourselves, that we are underlings."

University of Texas at Austin '23
Seven Lakes High School '19