A bicyclist climbs a hill 17 m tall and then coasts down the other side without pedaling. If the cyclist’s speed was 2.5 m/s at the top, what is it at the bottom (ignoring friction)?
what's the answer?
To find the speed of the cyclist at the bottom of the hill, we can use the principle of conservation of energy. At the top of the hill, the cyclist has potential energy, which is then converted into kinetic energy as they coast down.
The potential energy (PE) at the top of the hill is given by the formula:
PE = m * g * h
where:
m is the mass of the cyclist,
g is the acceleration due to gravity (approximately 9.8 m/s²),
h is the height of the hill.
Since we are given the height of the hill (h = 17 m), we need to determine the mass of the cyclist.
Next, the kinetic energy (KE) at the bottom of the hill is given by the formula:
KE = (1/2) * m * v²
where v is the velocity (speed) of the cyclist at the bottom of the hill.
According to the conservation of energy principle, the potential energy at the top equals the kinetic energy at the bottom (ignoring friction), so we can equate the two equations:
PE = KE
m * g * h = (1/2) * m * v²
We can simplify this equation by cancelling out the mass:
g * h = (1/2) * v²
Now we can solve for v, the velocity at the bottom of the hill:
v² = 2 * g * h
v = √(2 * g * h)
Substituting the known values:
v = √(2 * 9.8 * 17) m/s
Calculating the expression inside the square root:
v ≈ √(332.4) m/s
v ≈ 18.21 m/s
Therefore, the speed of the cyclist at the bottom of the hill, ignoring friction, is approximately 18.21 m/s.