Calvin and hobbes go for a sleigh ride.

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In summary, Calvina and Hobbes went for a sleigh ride from Point A to Point D, with a path that included a downhill slope of 30m height and 40m length (hypotenuse of 50m), a level surface of 60m, and an uphill slope of 30m height and 30m length. Using the equation Δd = v1Δt + 0.5aΔt^2, it was determined that the time from A to B was 4.1 seconds, and the time from B to C was 2.5 seconds. To calculate the time from C to D, the formula v(t) = v1 + a*t was used,
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nc9261
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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 :)

 
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  • #2
Hello, and welcome to PF!

Can you find the acceleration between C and D?
 
  • #3
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.
 

FAQ: Calvin and hobbes go for a sleigh ride.

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"Calvin and Hobbes go for a sleigh ride" is considered a beloved classic because of its relatable and humorous portrayal of childhood and imagination. The endearing friendship between Calvin and Hobbes and the beautifully drawn illustrations also contribute to its enduring popularity.

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