Skateboarding Physics: Min Speed, Optimal Ramp Angle & Displacement Vector

[kevin948]

Homework Statement

(Please check the attached file)

a)What is the minimum speed he requires to make it to the ramp?
b)What would be the best ramp angle so that the skateboarder lands as smoothly as possible?
c)What is the skateboarder’s displacement vector, average velocity vector, and average acceleration vector, between the moment the he leaves the ledge to the moment he reaches the other side?

Homework Equations

△y =Vi,y △t + ½ ay△t²

The Attempt at a Solution

I solved question A

-1 = -4.9△t²

0.45s

4m/0.45s = 8.8m/s

but I don't know how to solve question B and C

 

[Doc Al]

For B, how do you think the ramp angle should relate to his direction of motion? What is the skater's direction of motion?

 

[tomcue]

.


I would like to first clarify that the given information and equations are not enough to provide an accurate and complete solution to the problem. More information about the skateboarder's initial position, velocity, and acceleration is needed in order to accurately calculate the displacement vector, average velocity vector, and average acceleration vector.

However, based on the given information, here are some possible approaches to solving questions B and C:

b) To determine the best ramp angle for a smooth landing, we need to consider the forces acting on the skateboarder. As the skateboarder leaves the ledge and moves towards the ramp, gravity will be pulling them downwards while the ramp will provide an upward normal force. The optimal ramp angle would be one that balances these forces and allows the skateboarder to land smoothly. This can be achieved by setting the downward force due to gravity equal to the upward normal force provided by the ramp. The angle at which this occurs will depend on the mass of the skateboarder and the angle of the ramp.

c) The displacement vector, average velocity vector, and average acceleration vector can be calculated using the given equation and the values obtained in part A. However, as mentioned earlier, more information is needed to accurately calculate these vectors. Additionally, it is important to note that the skateboarder's motion will not be uniform, meaning their velocity and acceleration will be constantly changing due to the forces acting on them. In order to accurately calculate these vectors, we would need to know the skateboarder's position, velocity, and acceleration at multiple points in time during their motion.

In conclusion, while the given information allows us to solve part A, more information is needed to accurately solve parts B and C. Additionally, the solution to these questions would require a more thorough understanding of physics concepts such as forces, motion, and vectors.