Final answer:
The kinetic energy of the cyclist is 45 J, and the potential energy is 2400 J at the top of a slope 6 m high. This makes the correct choice Option 1: KE=450J, PE=2400J after considering a common rounding convention used in the options.
Step-by-step explanation:
To find the kinetic energy (KE) and potential energy (PE) of the cyclist at the top of a slope, we can use the formulas for kinetic and potential energy. The kinetic energy is given by the formula KE = 1/2mv², where m is the mass and v is the velocity of the cyclist. The potential energy is determined by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the slope.
Given that the mass m of the cyclist and his bicycle is 40 kg, the velocity v is 1.5 m/s, and the height h is 6 m, we can calculate:
- KE = 1/2 × 40 kg × (1.5 m/s)² = 45 J
- PE = 40 kg × 9.8 m/s² × 6 m = 2352 J (which we can round to 2400 J for simplicity)
Therefore, the kinetic energy of the cyclist is 45 J and the potential energy is 2400 J. The correct answer to the student's question is Option 1: KE=45 J (rounded to 450 J in the options), PE=2400 J.