Figure out how far up the incline of the hill the box slides.

In summary, the box at the bottom of the hill has a speed of 15 m/s and the hill forms a 30 degree angle with the horizontal. By using the equation d = (vf2 + vi2) / 2a and incorporating the component of gravity acting down the incline, the distance traveled up the incline is calculated to be 13.25 m. However, the correct answer is 23 m, which is obtained by using a different value for the acceleration due to gravity.
  • #1
jumbogala
423
4

Homework Statement


At the bottom of a hill, a box has a speed of 15 m/s. The hill forms an angle of 30 degrees with the horizontal. How far up the incline of the hill does the box slide?

Homework Equations


My answer:
d = (vf2 + vi2) / 2a

The Attempt at a Solution


vi = 15 m/s
vf = 0 m/s

a = (-9.81 m/s2)*cos(30) = -8.49 m/s2

d = 13.25 m

However, the answer key says d = 23 m. This is the answer if you use a = (9.81 m/s^2)*sin(30) instead. Help?
 
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  • #2
What's the component of gravity acting down the incline? That's where sinθ comes in.
 
  • #3
Oops, I had 30 degrees in the wrong corner of the triangle. It works now! Thanks.
 

Related to Figure out how far up the incline of the hill the box slides.

1. How can I determine the distance the box slides up the incline of the hill?

To determine the distance the box slides up the incline of the hill, you will need to use the formula d = h / sinθ, where d is the distance, h is the height of the incline, and θ is the angle of the incline. You will also need to know the coefficient of friction between the box and the incline.

2. What factors affect the distance the box slides up the incline?

The distance the box slides up the incline is affected by the height and angle of the incline, as well as the coefficient of friction between the box and the incline. Other factors such as the weight of the box and any external forces acting on it may also affect the distance.

3. Can I use a different formula to calculate the distance the box slides up the incline?

Yes, there are other formulas that can be used to calculate the distance the box slides up the incline. Some examples include the work-energy theorem and the laws of motion, which take into account factors such as the mass and velocity of the box.

4. How accurate are the calculations for determining the distance the box slides up the incline?

The accuracy of the calculations will depend on the accuracy of the measurements taken for the height and angle of the incline, as well as the coefficient of friction. It is important to use precise and consistent measurements for the most accurate results.

5. Are there any tools or equipment that can help me measure the distance the box slides up the incline?

Yes, there are tools and equipment that can help you measure the distance the box slides up the incline. Some examples include a protractor for measuring the angle of the incline, a ruler or measuring tape for measuring the height of the incline, and a scale for determining the weight of the box.

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