Question

A block is given a very brief push up a 20.0° frictionless incline to give it an initial speed of 12.0 m/s. (a) how far along the surface of the plane does the block slide before coming to rest?

Answer 1

First we calculate the time it took before coming to rest. We use the vertical component of velocity in this case. The formula is:

vy = v0 sinθ – g t

where, vy is final velocity at the peak = 0,  v0 sinθ = initial vertical velocity, g is acceleration due to gravity, t is time

therefore:

0 = 12 sin20 – 9.8 t

t = 0.4188 s

 

Then calculate the distance using the horizontal component:

d = v0 cosθ t

d = 12 cos20 * 0.4188

d = 4.72 m