How do I calculate the height on a ramp for a rolling ball?

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In summary, the problem involves a steel ball with a mass of 45 grams and a diameter of 2.2 cm, initially rolling at an unknown velocity up a 35 degree ramp. After turning 12 revolutions, the ball comes to a stop and the distance up the ramp is calculated to be 0.132m. The question is how to solve for the height above the ground that the ball reaches. By considering the ramp as a right triangle and using trigonometric relationships, the height can be calculated.
  • #1
sportsnh
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I am confused as to how i solve for height in this problem. I can solve for the distance up the ramp the ball goes but not for the height above the ground.

The problem states: A steel ball has a mass of 45 grams and a diameter of 2.2 cm. The ball is moving and rolling at an initial velocity (not known) when it starts rolling up a 35 degree ramp and comes to a stop after turning 12 revolutions.

I solved for how far up the ramp the ball went by taking the 12 rev *2π rad * .011m /1 rev / 2π rad and got .132m.

I have looked at all the equations that i have but can't figure out how to solve for how high the ball goes up?
 
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  • #2
right triangles

You have the angle of the ramp. Consider it as a right triangle--what trig relationships might relate height to distance up the ramp (which is the hypotenuse)?
 
  • #3
thanks...i knew it was something very simple that i was missing
 

1. How do you calculate height using the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, to solve for height, you can use the formula h = √(c² - a²), where h is the height, c is the length of the hypotenuse, and a is the length of the other side.

2. How do you solve for height when given the area and base of a triangle?

To solve for height in a triangle when given the area and base, you can use the formula h = (2 * area) / base. This formula is derived from the formula for the area of a triangle, which is A = (1/2) * base * height. By rearranging the formula, we can solve for height.

3. How do you use similar triangles to find the height of an object?

In similar triangles, corresponding sides are proportional. This means that if two triangles have the same angles, their sides will be in the same ratio. To use this concept to find the height of an object, you can set up a proportion with the known height and distance of a similar object, and then solve for the unknown height. For example, if two objects have the same angle of elevation and one has a known height of 5 feet and distance of 10 feet, while the other has a known distance of 20 feet, the unknown height can be found by setting up the proportion 5/10 = x/20 and solving for x, which would give a height of 10 feet.

4. How do you solve for height in a cylindrical object?

In a cylindrical object, the height can be found by dividing the volume by the area of the base. The formula for the volume of a cylinder is V = πr²h, where π is approximately 3.14, r is the radius, and h is the height. To solve for height, rearrange the formula to h = V / (πr²).

5. How do you solve for height in a right circular cone?

In a right circular cone, the height can be found using the Pythagorean theorem. The formula for the volume of a cone is V = (1/3) * πr²h, where r is the radius and h is the height. By rearranging this formula, we can solve for h, which gives h = √(3V / πr²). This formula can also be used to find the height of a cone when given the volume and radius.

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