A block is projected up a frictionless inclined plane with initial speed v0 = 7.14 m/s. The angle of incline is θ = 36.5°. (a) How far up the plane does it go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

Explanation:

Given data

For Part (a)

Starting with the -ve acceleration of the body (opposite to the gravitational force)

Using equation of motion

For Part (b)

Using the result in Part (a) we can substitute in other equation of motion to get time t:

For Part (c)

At state 2 where vo=0m/s and the acceleration is positive (same direction as the gravitational force)

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the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm