A 75g person on skis is going down a hill sloped at an angle 30.the coefficient of kinetic friction between the skis and the snow is 0.15.how fast is the skier going 10s after starting from rest?(answer=36m/s)

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To find the speed of the skier after 10 seconds, we can use the principles of Newton's laws and the concept of work and energy.

The first step is to determine the net force acting on the skier. The net force can be calculated using the equation:

Net Force = (mass of the skier) x (acceleration)

The acceleration of the skier can be determined by considering the forces acting on the skier:

1. The force of gravity: The force of gravity can be calculated using the equation:

Force of gravity = (mass of the skier) x (acceleration due to gravity)

F_gravity = (75g) x (9.8 m/s^2) = 735 N

2. The force due to kinetic friction: The force due to kinetic friction can be calculated using the equation:

Force of friction = (coefficient of kinetic friction) x (normal force)

The normal force is equal to the force perpendicular to the surface, which is given by:

Normal Force = (mass of the skier) x (acceleration due to gravity) x (cosine of the slope angle)

Normal Force = (75g) x (9.8 m/s^2) x (cos(30))

Next, we can plug in the known values:

Normal Force = (75 * 9.8) x (cos(30)) = 637.5 N

Now we can calculate the force of friction:

Force of friction = (0.15) x (637.5 N) = 95.63 N

Since the skier is moving downhill, the force of kinetic friction opposes the motion of the skier. Therefore, the net force can be calculated as:

Net Force = Force of gravity - Force of friction = 735 N - 95.63 N = 639.37 N

Now we can use Newton's second law, which states that the net force is equal to mass times acceleration:

Net Force = (mass of the skier) x (acceleration)

639.37 N = (75g) x (acceleration)

Solving for acceleration:

acceleration = (639.37 N) / (75g)

acceleration ≈ 8.525 m/s^2

Now, we can find the velocity of the skier after 10 seconds using the equation of motion:

velocity = initial velocity + (acceleration x time)

Since the skier starts from rest, the initial velocity is 0 m/s.

velocity = 0 + (8.525 m/s^2) x (10 s)

velocity = 85.25 m/s

However, this is the theoretical velocity of the skier after 10 seconds. Considering the coefficient of kinetic friction, the skier experiences a retarding force due to the friction, which reduces the velocity. To account for this, we need to subtract the distance traveled due to friction.

To calculate the distance traveled due to friction, we can use the equation:

distance = (initial velocity x time) - (0.5 x acceleration x time^2)

distance = (0 m/s) x (10 s) - (0.5 x 8.525 m/s^2) x (10 s)^2

distance = 0 - (42.625 m/s^2) x (100 s^2)

distance ≈ -4262.5 m (negative since it is opposing the motion of the skier)

Now we can subtract the distance traveled due to friction from the theoretical distance traveled without friction:

distance traveled without friction = (initial velocity x time) - (0.5 x acceleration x time^2)

distance traveled without friction = (0 m/s) x (10 s) - (0.5 x 8.525 m/s^2) x (10 s)^2

distance traveled without friction = 0 - (42.625 m/s^2) x (100 s^2)

distance traveled without friction ≈ -4262.5 m

Therefore, the actual distance traveled by the skier after 10 seconds is:

actual distance traveled = theoretical distance traveled - distance traveled due to friction

actual distance traveled = -4262.5 m - (-4262.5 m) = 0 m

Since the actual distance traveled is 0 m, it means the skier has come to rest due to the force of friction.

Therefore, the final speed of the skier after 10 seconds is 0 m/s, not 36 m/s as stated in the question. It seems there may have been an error in the question or calculations.