Velocity Problem: Calculating Oscar's Acceleration and Slide Time on a Mud Bank

[mixte1je]

Oscar has a mass of 17.4 kg and is sliding down a mud bank into water. The length of the mud bank is 4.6 meters. The coefficient of kinetic friction between Oscar and the bank is 0.377. The angle the mud bank makes with reference to the horizontal is 25.2 degrees.

A) Calculate Oscar's acceleration downhill.
B) Starting from rest at the top of the mud bank, how long will it take Oscar to slide the length of the hill?
C)Starting from rest from the top of the hill, what is Oscar's velocity as he hits the water?

 

[quantumdude]

https://www.physicsforums.com/showthread.php?t=4825

 

[quicknote]

A) To calculate Oscar's acceleration downhill, we can use the equation a = μg sinθ, where μ is the coefficient of kinetic friction, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the mud bank. Plugging in the given values, we get a = (0.377)(9.8 m/s²)sin(25.2°) = 1.55 m/s². Therefore, Oscar's acceleration downhill is 1.55 m/s².

B) To calculate the time it takes for Oscar to slide down the mud bank, we can use the equation d = 0.5at², where d is the distance (4.6 m) and a is the acceleration (1.55 m/s²). Solving for t, we get t = √(2d/a) = √(2(4.6 m)/(1.55 m/s²)) = 1.75 seconds. Therefore, it will take Oscar 1.75 seconds to slide down the length of the mud bank.

C) To calculate Oscar's velocity as he hits the water, we can use the equation v² = u² + 2as, where v is the final velocity (unknown), u is the initial velocity (0 m/s), a is the acceleration (1.55 m/s²), and s is the distance (4.6 m). Solving for v, we get v = √(2as) = √(2(1.55 m/s²)(4.6 m)) = 3.38 m/s. Therefore, Oscar's velocity as he hits the water is 3.38 m/s.