How Far Will a Cart Travel Up a Ramp at Different Angles?

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AI Thread Summary
The discussion focuses on calculating the maximum distance a frictionless cart will travel up a ramp at different angles, given an initial speed of 2.5 m/s. For a ramp angle of 20 degrees, the corrected maximum distance is approximately 0.932 meters, while for a 45-degree angle, it is about 0.4509 meters. Participants confirm the accuracy of the calculations, noting a significant initial error in the first response. The importance of checking mathematical work is emphasized throughout the conversation. The final answers reflect the correct application of physics equations related to motion on an incline.
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Homework Statement


A cart is pushed up a ramp with an initial speed v0=2.5m/s. For this problem, you may assume that the cart is frictionless and the acceleration of the cart a=gsin\theta.

A) If the angle of the ramp is \theta=20, what is the maximum distance d that the cart will travel up the ramp?

B) If the angle of the ramp is \theta=45, what is the maximum distance d that the cart will travel up the ramp?

Homework Equations


v2=v02+2a\DeltaX
manipulated to...
(v2-v02) / (2a) = \DeltaX

The Attempt at a Solution



A)
9.8sin(20)=3.351797
(0-(2.5)2) / (2(3.351797) = \DeltaX
\DeltaX=10.474 meters

B)
9.8sin(45)=6.9296
(0-(2.5)2) / (2(6.9296) = \DeltaX
\DeltaX=.4509 meters

I was feelin' good about the first answer but the second answer seems too low... did I do these correctly?
 
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Shameless bump.
 
Tonik said:
Shameless bump.
B looks good. Just check your math error in A.
 
PhanthomJay said:
B looks good. Just check your math error in A.

Tonik said:
A)
9.8sin(20)=3.351797
(0-(2.5)2) / (2(3.351797) = \DeltaX
\DeltaX=.93234 meters

Fixed, I have no idea how I came up with ~10 meters...
Thanks bud!
 

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