Question
A 1 kg rock is dropped from a cliff 90 meters high. After falling 20 meters, the kinetic energy of the rock is approximately what?
Answers
GPT 3.5
To find the kinetic energy, we need to know the velocity of the rock. We can find this using the equations of motion.
The initial velocity of the rock is 0 m/s as it is dropped from rest. The final velocity can be found using the equation:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration (which is due to gravity and equal to 9.8 m/s^2), and s is the displacement.
Plugging in the given values, we have:
v^2 = 0^2 + 2(9.8)(20)
v^2 = 392
v ≈ 19.8 m/s
Now we can find the kinetic energy using the equation:
Kinetic Energy = 1/2 * mass * velocity^2
Kinetic Energy = 1/2 * 1 kg * (19.8 m/s)^2
Kinetic Energy ≈ 196.02 Joules
Therefore, the kinetic energy of the rock after falling 20 meters is approximately 196.02 Joules.
The initial velocity of the rock is 0 m/s as it is dropped from rest. The final velocity can be found using the equation:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration (which is due to gravity and equal to 9.8 m/s^2), and s is the displacement.
Plugging in the given values, we have:
v^2 = 0^2 + 2(9.8)(20)
v^2 = 392
v ≈ 19.8 m/s
Now we can find the kinetic energy using the equation:
Kinetic Energy = 1/2 * mass * velocity^2
Kinetic Energy = 1/2 * 1 kg * (19.8 m/s)^2
Kinetic Energy ≈ 196.02 Joules
Therefore, the kinetic energy of the rock after falling 20 meters is approximately 196.02 Joules.