Ball and Ramp: Solving for Time and Evaluating Position

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In summary, changing the angle of the ramp affects the distance the ball travels, with steeper angles resulting in greater distance due to increased potential energy. The height of the ramp and the speed of the ball are directly proportional, as a higher ramp provides more potential energy for the ball to convert into kinetic energy. The weight of the ball does not significantly impact its trajectory when hitting the ramp, but may affect its distance traveled. If the ramp is not perfectly straight, the ball's trajectory will be affected by the force of gravity pulling it towards the center of the earth. The type of surface on the ramp can also affect the speed of the ball, with smoother surfaces resulting in faster speeds and rougher surfaces slowing it down. Other factors, such
  • #1
atomB
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This is from a practice exam without an answer key. I tried the problem once before and am getting a different solution now. My method is solving for the time t when the x position is the width of ramp, and then evaluating y(t) to see if it is more or less than the height of the ramp.

The problem statement, relevant equations, and attempt are in the image.

2dm6zie.jpg
 
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  • #2
That sounds like a reasonable method - what did you do before?
 
  • #3
atomB said:
2dm6zie.jpg
There is something missing from your equation for y(t)
 

FAQ: Ball and Ramp: Solving for Time and Evaluating Position

Does changing the angle of the ramp affect the distance the ball travels?

Yes, changing the angle of the ramp will affect the distance the ball travels. The steeper the angle of the ramp, the farther the ball will travel. This is due to the influence of gravity and the increased potential energy of the ball at a higher angle.

What is the relationship between the height of the ramp and the speed of the ball?

The height of the ramp and the speed of the ball are directly proportional. This means that as the height of the ramp increases, the speed of the ball also increases. This is because a higher ramp provides more potential energy for the ball to convert into kinetic energy, resulting in a faster speed.

How does the weight of the ball affect its trajectory when it hits the ramp?

The weight of the ball does not have a significant impact on its trajectory when it hits the ramp. As long as the ball has enough momentum to reach the top of the ramp, it will follow the same path regardless of its weight. However, a heavier ball may roll farther once it reaches the end of the ramp due to its increased mass and momentum.

What happens to the ball's trajectory if the ramp is not perfectly straight?

If the ramp is not perfectly straight, the ball's trajectory will be affected. This is due to the force of gravity pulling the ball towards the center of the earth, causing it to follow a curved path. The degree of curvature will depend on the angle and location of the curve in the ramp.

Does the type of surface on the ramp affect the speed of the ball?

Yes, the type of surface on the ramp can affect the speed of the ball. A smoother surface will result in less friction, allowing the ball to travel faster. On the other hand, a rougher surface will create more friction, slowing down the ball's speed. Other factors such as the material and shape of the surface can also impact the ball's speed.

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