Final answer:
To find the cyclist's speed at the bottom of the slope, we can use the principle of conservation of mechanical energy: the cyclist's initial potential energy is equal to the final kinetic energy at the bottom of the slope. After substituting the given values into the conservation of energy equation, the cyclist's speed at the bottom of the slope is approximately 18.5 m/s.
Step-by-step explanation:
To find the cyclist's speed at the bottom of the slope, we can use the principle of conservation of mechanical energy. At the top of the slope, the cyclist's initial potential energy is equal to the final kinetic energy at the bottom of the slope.
So we can equate:
Initial potential energy (mgh) + Initial kinetic energy (0) = Final potential energy (0) + Final kinetic energy (1/2mv^2)
The potential energy is given by mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the slope.
The kinetic energy is given by (1/2)mv^2, where m is the mass and v is the final velocity.
Using the given values:
Mass (m) = 70 kg
Height (h) = 30 m
Drag force (air resistance) = 11 N
Acceleration due to gravity (g) = 9.8 m/s^2
From the conservation of energy equation, we can solve for v, the final velocity at the bottom of the slope.
After substituting the values, we find that the cyclist's speed at the bottom of the slope is approximately 18.5 m/s.