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.