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A 20.0 kg box slides 1.60 m down a rooftop with a 30.0° incline and a...

A 20.0 kg box slides 1.60 m down a rooftop with a 30.0° incline and a coefficient of kinetic friction of 0.342. It then falls off the rooftop and hits the ground. Assume no air resistance. The bottom of the rooftop is 2.78 m above ground.

a) What are the components of the weight, using axes parallel and perpendicular to the rooftop?

b) Write the normal force and the force of friction in component form

c) Calculate the acceleration of the block

d) If the box has an initial speed of 0.607 m/s, what is the speed at the bottom of the rooftop?

e) The box slides off the roof and becomes a projectile. Now use horizontal and vertical axes instead of the previous axes. What are the horizontal and vertical components of the velocity the moment the box leaves the roof?

f) Use these components as the box’s new initial velocity. What are the components of the final velocity?

g) How much time does it take for the box to hit the ground?

h) How far next to the house does the box land?

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