How Does Physics Ensure a Safe Water Skier Stunt Over a Shark Tank?

AI Thread Summary
To ensure the water skier successfully clears the shark tank, the minimum speed at the ramp must be calculated considering both the ascent up the ramp and the subsequent projectile motion. While projectile motion principles apply, the skier's ascent introduces complexities that require additional information about the ramp's angle and height. The mass of the skier is irrelevant for determining the minimum speed, as the calculations can be made using energy conservation principles. The discussion highlights the importance of optimal ramp design to minimize required speed for safety. Ultimately, the problem is deemed unsolvable with the provided details, emphasizing the need for clearer parameters.
Bostonpancake0
Messages
42
Reaction score
0
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).
 
Physics news on Phys.org
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.
 
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
 
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!
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top