A box starts from rest and slides 40 m down a frictionless inclined plane. The total vertical displacement of the box is 20 m. How long does it take for the block to reach the end of the plane?

Using a simple pulley and rope system, a crewman on an Arctic expedition is trying to lower a crate of mass ?1=5.13 kg to the bottom of a steep ravine of height ?=22.5 m. The crewman of mass ?2=60.9 kg is walking while holding the rope, being careful to lower the crate at a constant speed of ?0=1.50 m/s. Unfortunately, when the crate reaches a point ℎ=12.5 m above the ground, the crewman steps on a slick patch of ice and slips. The crate immediately accelerates toward the ground, dragging the hapless crewman across the ice and toward the edge of the cliff. Assuming the ice is perfectly slick, so that there is no friction between the crewman and the ice once he slips and falls down, at what speed ?1 will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff, and that the pulley is frictionless. ?1=.     m/s   At what speed ?2 will the crewman hit the bottom of the ravine? Assume no…

A box with a mass of 7.24 kg is held at the top of frictionless inclined plane of length L = 10.9 m and an inclination angle 0 = 26.9 degrees above the horizontal. The box is released from rest and stops at a distanced = 22.62 m from the bottom of the inclined plane along the rough horizontal surface. What is the coefficient of kinetic friction between the box and the rough horizontal surface?

A boy shoves his stuffed toy zebra down a frictionless chute. It starts at a height of 1.63 m above the bottom of the chute with an initial speed of 1.41 m/s . The toy animal emerges horizontally from the bottom of the chute and continues sliding along a horizontal surface with a coefficient of kinetic friction of 0.273 . How far from the bottom of the chute does the toy zebra come to rest? Assume ?=9.81 m/s2 .