You push a \(2.0-\mathrm{kg}\) block up a ramp by exerting a \(100-\mathrm{N}\) force directed parallel to the ramp, which is at a \(30^{\circ}\) angle to the horizontal.

(a) Ignoring any effects due to friction, calculate the block's speed when you have pushed it \(2.0 \mathrm{~m}\) if its upward speed when you began pushing was \(2.0 \mathrm{~m} / \mathrm{s}\).

(b) Now consider friction. If the coefficient of kinetic friction between block and ramp is 0. 25 , what is the block's speed after you have pushed it \(2.0 \mathrm{~m}\) ?

(c) With this value of \(\mu_{k}\), how much farther up the ramp does the block move once you stop pushing after the \(2.0 \mathrm{~m}\) ?