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

Answer: 0.336 m