Ricky, the 5.8 kg snowboarding raccoon, is on his snowboard atop a frictionless ice-covered quarter-pipe with radius 9 meters. If he starts from rest at the top of the quarter-pipe, what is his speed at the bottom of the quarter-pipe?
Use SI units in your answer.
v_{Ricky} =
To find the speed of Ricky at the bottom of the quarter-pipe, we can use the principle of conservation of mechanical energy. At the top of the quarter-pipe, Ricky only has potential energy, and at the bottom of the quarter-pipe, all of his potential energy is converted into kinetic energy.
The potential energy of Ricky at the top of the quarter-pipe can be calculated using the formula:
PE = m * g * h
Where:
m = mass of Ricky = 5.8 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the quarter-pipe, which is the radius of the quarter-pipe = 9 meters
PE = 5.8 kg * 9.8 m/s^2 * 9 m
PE = 509.64 Joules
Since energy is conserved, the potential energy at the top of the quarter-pipe is equal to the kinetic energy at the bottom of the quarter-pipe.
The kinetic energy (KE) can be calculated using the formula:
KE = (1/2) * m * v^2
Where:
v = velocity of Ricky
Since Ricky starts from rest, his initial velocity (v) is 0.
Therefore, we have:
PE = KE
509.64 J = (1/2) * 5.8 kg * v^2
Simplifying the equation:
v^2 = (509.64 J * 2) / 5.8 kg
v^2 = 350.83 J/kg
Taking the square root of both sides:
v = sqrt(350.83 J/kg)
v ≈ 18.7 m/s
Therefore, Ricky's speed at the bottom of the quarter-pipe is approximately 18.7 m/s.