Question

8. A 55-kg skateboarder enters a ramp moving horizontally with a speed of 6.5 m/s, and leaves the ramp moving vertically with a speed of 4.1 m/s. (A) Find the height of the ramp, assuming no energy loss to frictional forces.

Answer 1

The maximum height above the bottom of the ramp is 1.3 m.

Step-by-step explanation:

Energy loss to friction

The energy lost to friction by the skateboarder is calculated from the change in kinetic energy of the skateboarder.

ΔK.E = K.Ef - K.Ei

ΔK.E = ¹/₂m(vi² - vf²)

ΔK.E = 0.5 x 55 (4.1² - 6.5²)

ΔK.E = -699.6 J

Maximum height above the bottom of the ramp

The maximum height above the bottom of the ramp is determined from conservation of energy.

mghi + ¹/₂mvi² = ¹/₂mvf² + mghf

55 x 9.8 x hi + (0.5 x 55 x 6.5²) = (0.5 x 55 x 4.1²) + (55 x 9.8 x 0)

539hi + 1161.88 = 462.28

539hi = -699.6

hi = -699.6/539

hi = -1.3 m

Thus, the maximum height above the bottom of the ramp is 1.3 m.