Calvin and hobbes go for a sleigh ride.

[nc9261]

Homework Statement

Calvina nd Hobbes go for a sleigh ride. They start from rest at Point a and proceed to point D along the path ABCD. AB is a downhill slope of height 30m and length 40 m (thus hypotenuse where they ride on is 50m), BC is level surface 60m and CD is an uphill slope of hieght 30m and length 30m. The surfaces are all frictionless. Calculate how long the trip from A to D took.

Homework Equations

Δd= v1 Δt +0.5a *Δ t^2

The Attempt at a Solution

acceleration from A to B is equal to gsintheta from free body diagram. theta is 37 degrees.
using equation above, time for A to B is 4.1 seconds.

B to C is constant velocity because net force is 0. therefore, time is 60 divided by final velocity of AB which is 24m/s. therefore 60/24 is 2.5

Then I am stuck on time for CD.
If anyone can help, thanks so much :)

 

[TSny]

Hello, and welcome to PF!

Can you find the acceleration between C and D?

 

[rude man]

What you did was correct.

So use your formula for d again. What is d this time? what is v1? and what is a? This time you need to solve a quadratic since v1 is not zero the way it was at A.

You can avoid the quadratic by realizing v(t) between C and D is v1 + a*t. Let T be the time going from C to D, then v(T) = V(D) = v1 + a*T. Remember a is negative. What would V(D) be? Use energy conservation in going from A to D to answer that question, then solve for T.