A 5kg rock falls off of a 10m cliff. If air resistance exerts a force of 10N, what is the kinetic energy when the rock hits the ground?
A. 400J
B. 12.6m/s
C. 100J
D. 500J
To find the kinetic energy of the rock when it hits the ground, we need to consider the work done on the rock as it falls.
Work is defined as the force applied to an object multiplied by the displacement of the object in the direction of the force. In this case, the force applied is the gravitational force, which can be calculated using the formula F = mg, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The gravitational force acting on the rock is mg = 5 kg * 9.8 m/s^2 = 49 N. However, there is also air resistance acting against the motion of the rock, which exerts a force of 10 N in the opposite direction. Therefore, the net force acting on the rock is 49 N - 10 N = 39 N.
The kinetic energy of the rock can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
To find the velocity of the rock when it hits the ground, we can use the equation of motion s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time taken.
In this case, the displacement is 10 m (the height of the cliff). The initial velocity is 0 m/s as the rock is initially at rest. The acceleration is the acceleration due to gravity, -9.8 m/s^2 (negative because it acts in the opposite direction to motion), and the time taken can be found using the equation v = u + at.
Using v = u + at, we can solve for the time taken: 0 + (-9.8 t) = 0, which gives us t = 0 seconds. This implies that the rock takes no time to fall to the ground.
Since the time taken is 0 seconds, the final velocity v is also 0 m/s. Therefore, the kinetic energy of the rock when it hits the ground is KE = (1/2)mv^2 = (1/2) * 5 kg * (0 m/s)^2 = 0 J.
None of the given options match the calculated value of 0 J. Therefore, none of the provided options are correct.