With what velocity will a 22 kg sled be moving when it reaches the bottom of a 28 m hill?
To calculate the velocity of the sled at the bottom of the hill, we can use the principle of conservation of energy. As there is no mention of friction or other external forces, we can assume that only potential and kinetic energy are involved.
The potential energy (PE) at the top of the hill will be fully converted to kinetic energy (KE) at the bottom. The equations for potential and kinetic energy are as follows:
PE = m * g * h
KE = 0.5 * m * v^2
Where:
m is the mass of the sled (22 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height of the hill (28 m)
v is the final velocity of the sled at the bottom
Since the potential energy is converted entirely into kinetic energy, we can equate the equations:
PE = KE
m * g * h = 0.5 * m * v^2
Simplifying the equation:
22 kg * 9.8 m/s^2 * 28 m = 0.5 * 22 kg * v^2
6156 J = 11 kg * v^2
Dividing both sides by 11 kg and taking the square root:
561 J / 11 kg = v^2
510.55 m^2/s^2 = v^2
v = ā(510.55 m^2/s^2)
v ā 22.6 m/s
Therefore, the sled will be moving with a velocity of approximately 22.6 m/s when it reaches the bottom of a 28 m hill.