A block is pushed up a 20 degree frictionless incline with an initial speed 12.0 m/s. How high up the plane does the block slide

initial-speed
degree-frictionless

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A block is pushed up a 20 degree frictionless incline with an initial speed 12.0 m/s. How high up the plane does the block slide before coming to rest? And how much time does it take to return to its starting position

Answer:

the force on the block (parallel to the plane) is … m g sin(20º)

so the acceleration is … g sin(20º)

the time to peak (t) is … t = 12.0 / [g sin(20º)]

the average velocity is … (12.0 + 0) / 2

the height up the plane is … average velocity times the time

time up equals time down