A8.75-kg block is sent up a ramp inclined at an angle θ = 30.5° from the horizontal. it is given an initial velocity v0 = 15.0 m/s up the ramp. between the block and the ramp, the coefficient of kinetic friction is μk = 0.353 and the coefficient of static friction is μs = 0.639. how far up the ramp (in the direction along the ramp) does the block go before it comes to a stop?

14.1 meters.

ExplanationWeight on the block: .Consider the weight on the block as two components: along the slope and normal to the slope. Magnitude of the component along the slope: .Normal force on the block, which is the same as the component of weight normal to the slope: .Kinetic friction: .Maximum Static friction: .

. As a result, the block won't slip downwards after it comes to a stop.

As the block moves upward:

Net force on the block .Acceleration of the block: .Initial velocity .Final velocity of the block as it comes to a stop, given that it doesn't slip downwards.

How far does the block move in this process?

(3 sig. fig.).