Predicting a target for a ramp, using projectile motion and dynamics

[emma3001]

Homework Statement

I have this question where I need to determine how high up to place a metal ball on a ramp, having been given the ramp's target. The mass of the metal ball is 66.62g. To make things even more complicated, near to the end of the ramp, there is a loop-the-loop. The ramp ends at an angle of 17 degrees and the length of the upwards ramp at the end is 0.285m. How do I know the height at which to put the ball on the ramp?

Homework Equations

range x g= (initial velocity)squared x sin2(17 degrees)

The Attempt at a Solution

I thought that I could get the initial velocity by using the above equation but I now realize that that is assuming that the y displacement is zero but the loop-the-loop is lower (in a sink) than where the ball lands (on the table).

 

[AvroArrow]

I think that I might need to use conservation of energy equations, but I am not sure how to go about doing that. Any help would be greatly appreciated!

 

[ogb p]

As a scientist, there are a few things to consider when trying to predict a target for a ramp using projectile motion and dynamics. First, it is important to understand the basic principles of projectile motion, such as the equations for range and initial velocity. However, as mentioned in the question, these equations assume a flat, level surface and do not take into account the loop-the-loop at the end of the ramp. Therefore, it may be necessary to modify these equations or use a different approach to accurately predict the target.

One possible solution could be to break down the problem into smaller parts and analyze the motion of the metal ball separately for each section of the ramp. For example, you could calculate the initial velocity and trajectory for the first section of the ramp, up until the loop-the-loop, and then calculate the velocity and trajectory for the second section after the loop-the-loop.

Another approach could be to use computer simulations or experimental data to determine the necessary initial velocity and trajectory for the ball to successfully make it through the loop-the-loop and reach the target. This would require a more in-depth understanding of the dynamics involved, as well as precise measurements and data analysis.

In conclusion, predicting a target for a ramp using projectile motion and dynamics can be a complex problem, especially when there are additional obstacles or variations in the surface. It may require breaking down the problem into smaller parts, using experimental data, or using more advanced mathematical and computational methods to accurately predict the target.