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A bicycle and rider going 11 m/s approach a hill. Their total mass is 88 kg. (a) What is their kinetic energy? J (b) If the rider coasts up the hill without pedaling, how high above its starting level will the bicycle be when it finally rolls to a stop? m

User Lavita
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To calculate the kinetic energy of the bicycle and rider, we can use the formula:

Kinetic energy (KE) = 1/2 * mass * velocity^2

Given that the total mass is 88 kg and the velocity is 11 m/s, we can substitute these values into the formula:

KE = 1/2 * 88 kg * (11 m/s)^2

Calculating the expression inside the parentheses:

KE = 1/2 * 88 kg * 121 m^2/s^2

Simplifying the equation:

KE = 4844 kg m^2/s^2

Therefore, the kinetic energy of the bicycle and rider is 4844 Joules (J).

To determine how high above its starting level the bicycle will be when it finally rolls to a stop, we need to consider the conversion between kinetic energy and potential energy.

The potential energy (PE) is given by the equation:

PE = mass * gravity * height

where gravity is approximately 9.8 m/s^2.

Since the bicycle is rolling to a stop, its final kinetic energy will be converted entirely into potential energy when it reaches its highest point.

Equating the initial kinetic energy to the final potential energy:

KE = PE

Substituting the values:

4844 J = 88 kg * 9.8 m/s^2 * height

Simplifying the equation:

height = 4844 J / (88 kg * 9.8 m/s^2)

Calculating the expression:

height = 5.5 m

Therefore, the bicycle will be approximately 5.5 meters above its starting level when it finally rolls to a stop.

User Mazlix
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