Inclined Planes, finding final velocity

In summary, the conversation discussed a problem in which the height of an incline was determined using the sine law and then used in an equation to calculate the final velocity. The textbook's answer for the final velocity was incorrect, but the issue may be due to errors in the book. The book was identified as Physics 11, published by McGraw-Hill Ryerson.
  • #1
ericcy
19
1
Homework Statement
A 1975kg car is parked at the top of a steep 42m long hill inclined at an angle of 15 degrees. If the car starts rolling down the hill, how fast will it be going when it reaches the bottom of the hill (neglect friction).
Relevant Equations
Ei=Ef, Ek=1/2mv^2, Ep=mgh
I determined 42m to be the hypotenuse so I used sine law to find the height of the incline, 10.87m. I used this height in the equation Ei=Ef, since they should be equal.

Ei=Ef
mgh=1/2mv^2 (at the start there is no kinetic energy, at rest. at the end there is only kinetic, no potential)
1975(9.81)(10.87)=1/2(1975)v^2
210603.532/987.5=987.5v^2/987.5
(square root)213.269=(square root)v^2
V=14.603

Answer in the back of the book is 0.4m/s, for whatever reason. All responses are appreciated, thanks.
 
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  • #2
Your result looks good to me. Assuming that the statement of the problem is a full and correct representation of the textbook's version, then I suspect that the book's answer key may be mistaken for this problem.
 
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  • #3
@ericcy, can you let us know the title and publisher of your textbook so that we Mentors and Homework Helpers can keep an eye out for similar issues?

If we see a pattern of such typos or content errors related to a given text we can often shorten the time-to-resolution of questions where the calculated results don't match the text's answers. Thaks for your help!
 
  • #4
gneill said:
@ericcy, can you let us know the title and publisher of your textbook so that we Mentors and Homework Helpers can keep an eye out for similar issues?

If we see a pattern of such typos or content errors related to a given text we can often shorten the time-to-resolution of questions where the calculated results don't match the text's answers. Thaks for your help!
Turns out for this one I was just looking in the wrong section, lol. But there are quite a few mistakes in the back of the book that I've noticed. That's kind of why I've been asking a lot of questions on here to make sure that I'm right and the book is wrong.

The title of the book is Physics 11, publisher is McGraw-Hill Ryerson
 
  • #5
Thank you for your reply. This kind of information is very helpful for us here at PF.

Cheers!
 
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FAQ: Inclined Planes, finding final velocity

How do inclined planes affect the final velocity of an object?

Inclined planes affect the final velocity of an object by changing the acceleration. Objects on inclined planes experience a component of their weight that acts in the direction of the slope, which causes the object to accelerate and increase in velocity.

What is the equation for finding final velocity on an inclined plane?

The equation for finding final velocity on an inclined plane is Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time elapsed.

How does the angle of the inclined plane affect the final velocity?

The angle of the inclined plane affects the final velocity by determining the magnitude of the acceleration. The steeper the angle, the greater the component of the object's weight that acts in the direction of the slope, resulting in a higher acceleration and final velocity.

Can an object on an inclined plane ever reach a final velocity of zero?

Yes, an object on an inclined plane can reach a final velocity of zero if the angle of the slope is shallow enough and the object experiences enough friction. This would result in a balanced force situation where the object's weight is equal to the frictional force, causing it to come to a stop.

How does the mass of an object affect its final velocity on an inclined plane?

The mass of an object does not directly affect its final velocity on an inclined plane. However, a heavier object will have more weight, which will result in a greater force of acceleration and a potentially higher final velocity compared to a lighter object. The angle of the slope and the amount of friction also play a role in determining the final velocity.

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