Calculating Speed on a Ramp: Related Rates Problem

[fogvajarash]

Homework Statement

A girl enters a ramp with a speed of 30ft/s. The ramp has 4ft in height and 15ft in length. Calculate the speed at which she comes out of the ramp.

Homework Equations

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The Attempt at a Solution

I was thinking of just using cosθ=x/z, and just plugging in the values of the derivative (when she enters the ramp) and the value of the length of the ramp and the diagonal distance (finding cosθ with tan^-1θ; which gives me a final result of 8. However is this solution right? I'm not sure if my procedure is correct (and i don't have the answer to the exercise).

 

[jfizzix]

If the ramp is frictionless, you can use conservation of energy to figure out the change in her kinetic energy from the change in her gravitational potential energy.

E_{total} = K + U = \text{Const}

\Delta E_{total} = \Delta U + \Delta K =0

\Delta U = mg (z_{f}-z_{i})

\Delta K = \frac{1}{2}m (v_{f}^{2}-v_{i}^{2})

By knowing her initial speed and her change in height, you can figure out her final speed.

 

[fogvajarash]

I've also used that equation, but they are asking me to use calculus and not physical concepts. That's why I'm lost.

 

[Doc Al]

I've also used that equation, but they are asking me to use calculus and not physical concepts. That's why I'm lost.

You'll need to use some physical concepts, since this is a physics problem. If you want to use calculus, start with the acceleration and see if you can derive the appropriate kinematic formula.

 

[HallsofIvy]

There's a lot left out here! "A girl enters a ramp". Is the girl riding a car, a bicycle, or a horse? Or is she walking? Are we to assume that she (or her car or horse) does not exert any energy to get up the ramp?

 

[fogvajarash]

There's a lot left out here! "A girl enters a ramp". Is the girl riding a car, a bicycle, or a horse? Or is she walking? Are we to assume that she (or her car or horse) does not exert any energy to get up the ramp?

She's a waterskier and enters the ramp. I'm not really sure what the problem is asking for, as it only gives out that basic information. If it's in a Calculus textbook, i really doubt i have to apply physical concepts.