A block slides down a frictionless inclined ramp and experiences no significant air resistance. If the ramp angle is 17 degrees above the horizontal and the length of the surface of the ramp is 20.0 m find the speed of the block as it reaches the bottom of the ramp assuming that it started from rest.

10.71m/s

Explanation:

Mechanical energy is conserved since the ramp surface had no friction and the experiences no significant air resistance

Potential energy at the top of the ramp = mgh

where m is m, g = 9.8 m/s² ( acceleration due to gravity ) and h is height

since the length of the surface L of the ramp is 20.0 m and it is inclined at 17°

h, height = Lsinθ = 20 sin 17° = 5.85 m

kinetic energy of the block = mv²

potential energy = kinetic energy

m × 9.8 × 5.85 m = mv²

cancel m on both side

v = √(2 × 9.8 × 5.85) = 10.71m/s

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