Work and Energy at water park

[Bostonpancake0]

You've taken a summer job at a water park. In one stunt, a water skier is going to glide up the 2.0m high frictionless ramp, then sail over a 5.0m wide shark tank. You will be driving the boat that pulls her to the ramp. She'll drop the tow rope at the base of the ramp as you veer away. What minimum speed must you have as you reach the ramp such that she survive?.


Two questions: Why can't I use projectile motion to find her minimum horizontal speed?, and how do I solve this without projectile motion with little information (e.g her mass).

 

[mfb]

There is some information about the ramp missing to solve the problem.
The free fall can be solved like a projectile motion, but you have to consider that the skier has to climb the ramp first, too.

Here is the mass: m.
You don't need a numerical value to solve the problem.

 

[ehild]

You have to use projectile motion, but you do not need the mass.
You can assume that the angle of the ramp is set to optimum, so as the skier needs the minimum speed to overcome the shark tank.

ehild

 

[rude man]

You can assume the optimim angle of the ramp but I would run to the instructor and tell him his problem is unsolvable with the given information also!

 

[Nickie]

As a scientist, it is important to approach problems with critical thinking and thorough analysis. In this scenario, it is not appropriate to use projectile motion to find the minimum horizontal speed for the water skier to survive. This is because projectile motion assumes that there are no external forces acting on the object, and in this case, there are external forces such as air resistance and the force of the boat pulling the skier.

To solve this problem without using projectile motion, we can use the principles of work and energy. The skier needs to have enough kinetic energy to overcome the gravitational potential energy as she glides up the ramp and enough horizontal velocity to clear the shark tank. We can calculate the minimum speed needed using the conservation of energy principle.

First, we need to determine the potential energy of the skier at the top of the ramp. This can be calculated using the formula PE = mgh, where m is the mass of the skier, g is the acceleration due to gravity, and h is the height of the ramp. Since the ramp is frictionless, we can assume that all of the skier's initial potential energy will be converted into kinetic energy.

Next, we can calculate the kinetic energy needed for the skier to clear the shark tank. This can be calculated using the formula KE = 1/2mv^2, where m is the mass of the skier and v is the minimum horizontal velocity needed.

Finally, we can equate these two energies and solve for v. This will give us the minimum horizontal velocity needed for the skier to survive the stunt without using projectile motion or knowing the skier's mass.

In conclusion, as a scientist, it is important to approach problems with the appropriate tools and methods. In this scenario, using the principles of work and energy is a more suitable approach to determine the minimum speed for the skier to survive the stunt at the water park.