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

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Homework Help Overview

The problem involves a cart being pushed up a frictionless ramp at different angles, specifically 20 degrees and 45 degrees. The initial speed of the cart is given, and participants are tasked with calculating the maximum distance the cart travels up the ramp for each angle using the provided equations of motion.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of kinematic equations to determine the distance traveled by the cart at specified angles. There is an attempt to verify calculations and address concerns about the plausibility of the results, particularly for the 20-degree angle.

Discussion Status

Some participants have confirmed the calculations for the 45-degree angle, while others are questioning the accuracy of the results for the 20-degree angle, suggesting a potential math error. There is an ongoing effort to clarify and correct the calculations presented.

Contextual Notes

Participants are working under the assumption that the ramp is frictionless and are using specific values for gravitational acceleration. The discussion reflects a need for careful verification of mathematical steps in the context of the problem.

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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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