Launching a ball on a ramp

  • Thread starter lizette
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    Ball Ramp
In summary, the ball will land on the ramp rather than the plateau. The magnitude of its displacement will be less than 6m, and the angle of its displacement from the launch point will be different from the initial angle of 50 degrees. To determine the exact displacement and angle, you can use the equation for the ramp and equate it to the trajectory equation.
  • #1
lizette
I am having trouble figuring out this problem:

A ball is launched with a velocity of 10 m/s at an angle of 50 deg to the horizontal. The launch point is at the base of a ramp of horizontal length d1 = 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. a) Does the ball land on the ramp or the plateau? When it lands, what are b) the magnitude and c) the angle of its displacement from the launch point?

The diagram that I was given looked like this


--------/|--------
-------/ |
------/--d2
-----/---|
___o/-d1--

note: please ignore the ---- along the left side of the ramp, it was the only way i could figure out how to create the picture. the o = the ball. it's on the ground. the --- lines to the right of the ramp is the plateau.

I was using the trajectory equation:

y = (tan@)x - gx^2/2(Vocos@)^2
= (tan50)(6) - 9.8(6)^2/2(10cos50)^2
= 2.88 m

Then I found the length of the ramp:

ramp = d = (3.6^2 + 6^2)^(1/2) = 36.5 m

With this in mind, I was thinking that the ball would land on the ramp because 2.88 m does not even come close to clearing the length of the ramp, 36.5 m. So, would the magnitude of the displacement be 2.88 m? Concerning the angle, why would it be any different from 50 deg? I think that I'm getting confused about what they're looking for. Could someone help me understand this, please? Thanks so much
 
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  • #2
First off, your 2.88m is the height of the ball at a horizontal distance of 6m from the launch point.

Second, the length of the ramp would be
6.997m not 36.5 ( you used 36 instead of 3.6 when you calculated your formula)

Besides that, you don't need the length of the ramp.

Now since 2.88m is less than the 3.6m height of the ramp, the ball will land on the ramp.

The displacement will be the distance the ball has traveled horizontally when it hits the ramp. (it will intersect the ramp at some point short of 6 meters horizontal displacement.)

If you are looking the angle from horizontal the ball is traveling when it strikes the ramp, it won't be 50°. It would only be 50° if the ball landed at the same height as it was launched. Since it lands at a higher height, the angle will be different.

My advice would be to determine the equation that describes the ramp then equate this to the trajectory formula to find x where the values for y are the same for each equation.

From this you can get both the horizontal and vertical displacement for the ball when it strikes the ramp and then the angle of the path of the ball at that point.
 
  • #3


Based on the information given, it seems that the ball will indeed land on the ramp rather than the plateau. Your calculations for the height of the ball's trajectory (2.88 m) and the length of the ramp (36.5 m) support this conclusion.

As for the magnitude and angle of the ball's displacement, they will depend on the point at which the ball lands on the ramp. If the ball lands at the end of the ramp, then the magnitude of the displacement would be the same as the height of the trajectory (2.88 m) and the angle would be 50 degrees (the same as the launch angle). However, if the ball lands at a point before the end of the ramp, then the magnitude and angle of the displacement would be different.

To find the exact values, you would need to use the equation for displacement, which takes into account both the horizontal and vertical components of the ball's motion. This can be calculated using the velocity and time at which the ball lands on the ramp.

In summary, it seems that the ball will land on the ramp and the magnitude and angle of its displacement will depend on the point of impact. I hope this helps clarify the problem for you. Keep up the good work!
 

1. How does the height of the ramp affect the distance the ball travels?

The height of the ramp directly affects the potential energy of the ball. As the ramp height increases, the potential energy of the ball also increases, resulting in the ball traveling a farther distance. This relationship can be explained by the principle of conservation of energy, where the potential energy is converted into kinetic energy as the ball rolls down the ramp.

2. How does the angle of the ramp affect the speed of the ball?

The angle of the ramp affects the speed of the ball by influencing the component of the force of gravity that is parallel to the ramp. As the angle increases, the force of gravity acting on the ball also increases, resulting in a higher acceleration and ultimately a higher speed. However, there are other factors such as friction and air resistance that can also affect the speed of the ball.

3. How does the weight of the ball affect its motion on the ramp?

The weight of the ball affects its motion on the ramp by influencing the force of gravity acting on the ball. A heavier ball will experience a greater force of gravity and therefore will accelerate faster down the ramp. However, the weight of the ball also affects the amount of friction it experiences, which can also impact its motion on the ramp.

4. What role does friction play in the ball's movement on the ramp?

Friction plays a crucial role in the ball's movement on the ramp. As the ball rolls down the ramp, it experiences friction from the surface of the ramp, which can slow down its motion. This frictional force increases as the angle of the ramp increases and can significantly impact the distance and speed of the ball. Additionally, friction can also cause the ball to rotate or bounce, which can affect its trajectory.

5. How can we calculate the speed and distance of the ball on the ramp?

The speed and distance of the ball on the ramp can be calculated using equations from Newton's laws of motion and the principles of conservation of energy. These calculations take into account factors such as the angle and height of the ramp, the weight of the ball, and the coefficient of friction between the ball and the ramp. Additionally, experiments can also be conducted to measure the speed and distance of the ball under various conditions on the ramp.

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