Is My Kinematics Problem-Solving Approach Correct?

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SUMMARY

The discussion focuses on the correctness of solutions to three kinematics problems involving projectile motion and tension in cables. Problem 1 involves a ball fired from a height of 3.0m with an initial speed of 13m/s at a 22-degree angle below the horizontal, requiring calculations for impact time and velocity. Problem 2 addresses the tension in two massless cables supporting a 28kg sign. Problem 4 examines a system with two masses (m1 = 0.30kg, m2 = 0.45kg) on an incline with a coefficient of friction (mu = 0.40), necessitating the determination of acceleration and string tension.

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chrisfnet
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I was wondering, given my solutions and the problem statements; if someone could look over my work to see if there are any incorrect solutions/processes.

Thanks!
 

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Problem 1

A ball is fired from a height of 3.0m above the ground, with a speed of 13m/s and an angle of 22 below horizontal. At what time does the ball hit the ground? What is the impact velocity?

Problem 2

A 28kg sign is suspended by two massless cables. Find the tension in each.

Problem 4

In the setup shown, m1 = 0.30kg, m2 = 0.45kg and theta = 11. Also, between the first block and incline, mu = 0.40. Assume the system moves so that the first block slides up the incline. What is the acceleration of the system? What is the tension in the string?
 

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