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1) An archer fires an arrow from a bow. The arrow’s mass is 0.088 kg, and...

1) An archer fires an arrow from a bow. The arrow’s mass is 0.088 kg, and an average force of 110 N is exerted by the bowstring over a 0.78 m distance. Calculate the velocity of the arrow just after it is released by the bowstring by two methods:

a) Calculate the arrow’s acceleration that is caused by the bowstring, and use kinematic equations to calculate the velocity at the end of the acceleration. Assume a constant acceleration that corresponds to the given average force.

b) Use the work‐energy theorem to calculate the velocity.

2) A roller coaster car starts from rest at the top of a hill 15 m high and rolls down to ground level. From there it starts into a vertical loop. Exactly at the top of the loop it is 10 m high and the radius of the curvature of the track is 4.0 m. Assuming negligible friction and air resistance, what is the magnitude of the normal force acting on a 65 kg passenger at the top of the loop?

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