Question

1) A car has a mass of 34 kg and a velocity of 40.7 m/s. What is its kinetic energy in J?

2) A roller coaster is at rest (stopped) and then falls 49 meters.
What is the roller coaster speed at the bottom?

Answer 1

1) 28,160.33 J

2) 30.99 m/s

Explanation:

1)

Kinetic energy is given by the formula ...

KE = 1/2mv^2 . . . . . m represents mass

KE = (1/2)(34 kg)(40.7 m/s)² = 28,160.33 J

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2)

The potential energy is converted to kinetic energy.

mgh = 1/2mv² . . . . m represents mass

v = √(2gh) . . . . . . m cancels when we multiply by 2/m.

v = √(2·9.8 m/s²·49 m) ≈ 30.99 m/s . . . . . m represents meters

The speed at the bottom is about 30.99 m/s.

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Additional comment

Rounding to 2 significant digits, the answers would be ...

28,000 J

31 m/s