How can I solve for time in a pulley and ramp problem without a given variable?

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SUMMARY

The discussion focuses on solving a physics problem involving two masses connected by a pulley system, specifically a 5kg mass on a frictionless ramp and a 10kg hanging mass. The user derived the tension in the cable as T = -m1a + 98N and calculated acceleration as a = (98N - 49sin(θ))/15. The challenge lies in determining the time taken for the masses to move 3m without knowing the ramp angle (θ). The correct answer provided in the textbook is 1.13 seconds, which can be approached using kinematic equations if the ramp angle is known.

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Students studying physics, particularly those focusing on mechanics, as well as educators looking for problem-solving strategies in dynamics involving pulleys and inclined planes.

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Homework Statement



A mass [itex]m{1}[/itex] = 5kg is on a frictionless ramp and connected to a cable that passes over a pulley which is then attached to a second hanging mass, [itex]m{2}[/itex] = 10kg. How long will it take the boxes to move 3m if they are released from rest?

[itex]F{A}[/itex]= Forces acting on hanging object
[itex]F{B}[/itex]= Forces acting on object on ramp

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Homework Equations



F=ma

The Attempt at a Solution



I have solved for T using the force equation on object A and got T= -m1a + 98N

Then I substituted for T in the equation for object B and solved for acceleration, yielding:a=(98N-49sin[itex]\vartheta[/itex])/15

My biggest problem is, the book says the answer is 1.13 seconds. How can I solve in terms of seconds without another variable provided? I can't think of a way to use elimination to solve for [itex]\vartheta[/itex].
 
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The image didn't come out.

But as to your question - assuming your are given the ramp angle - hint: kinematic equations.
 

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