A block slides down a frictionless inclined ramp and experiences no significant air resistance. If the ramp angle is 17.0° above the horizontal and the length of the surface of the ramp is $20.0 \mathrm {~m}$ find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.
A) 10.7 m/s
B) 114 m/s
C) 7.57 m/s
D) 19.6 m/s

Question

Quizplus · Accepted Answer

The speed of the block can be found using energy conservation. The potential energy at the top is converted to kinetic energy at the bottom. The height $ h $ of the ramp can be found using $ h = 20.0 \sin(17.0°) $. The speed $ v $ is given by $ v = \sqrt{2gh} $, where $ g = 9.8 \, \mathrm{m/s^2} $. Calculating gives approximately 10.7 m/s.

A Block Slides Down a Frictionless Inclined Ramp and Experiences 20.0 m20.0 \mathrm {~m}20.0 m

A Block Slides Down a Frictionless Inclined Ramp and Experiences $20.0 \mathrm {~m}$