Suppose a metal sphere is launched up a ramp with vi=1.5 m/s. the end of the ramp is 1.20 m above the floor. the ramp is at an angle of 20° to the horizontal. calculate the range of the sphere.

The sphere will go up until all the initial kinetic energy be transformed into potential energy.

Intital kinetic energy = m*(vi)^2 / 2

Final potential energy = mgh

mgh = m(vi)^2 / 2 => h = (vi)^2 / (2g)

g = 9.81 m/s^2
vi = (1.5m/s)^2

h = (1.5m/s)^2 / (2*9.81m/s)^2 = 0.115 m

The range is the distance run over the ramp

Using trigonometry, sin(20°) = h /run => run = h / sin(20) = 0.115m / sin(20) = 0.336 m

0.336 m