# .A bike rider approaches a hill with a speed of 8.5m/s. The total mass of the bike and rider is 85kg. a.Find the kinetic energy of the?

.A bike rider approaches a hill with a speed of 8.5m/s. The total mass of the bike and rider is 85kg.

a. Find the kinetic energy of the bike and rider before going up the hill.

b.The rider coasts up the hill. Assuming there is no friction, at what height will the bike come to a stop?

c.Does your answer depend on the mass of the bike and rider? Explain.

Relevance

a.

K.E.

= (1/2) m v²

= (1/2) × 85 × (8.5)

= 360 N (to 2 sig. fig.)

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b.

Take g = 9.8 m/s

Gain in P.E. = Loss in K.E.

m g h = (1/2) m v²

g h = (1/2) v²

h = (1/2) v² / g

Height, h

= (1/2) (8.5)² / (9.8)

= 3.7 m (to 2 sig. fig.)

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c.

In part a, the answer depends on the total mass of the bike and the rider, as K.E. = (1/2) m v².

In part b, the answer does not depend on the mass of the bike and the rider, because m is canceled on the both sides. m disappears in the equation: h = (1/2) v² / g.