A rock tumbles straight down from a cliff, its moving at 20 m/s when it hits. What is the height of the cliff? The mass of the rock is 8 kg.
a) 2.5 m
b) 400 m
C) 20.4 m
d) 160 m
v = g t
20 = 9.81 t
t =2.03 seconds
h = (1/2) g t^2
h = 4.9 (2.03)^2
h = 20.4 meters
What's the time?
yolo
To find the height of the cliff, we can use the concept of gravitational potential energy (GPE) and kinetic energy (KE).
1. Calculate the initial kinetic energy:
The kinetic energy of the rock just before it hits the ground is given by the formula KE = (1/2) * m * v^2.
Where m is the mass of the rock (8 kg) and v is the velocity of the rock (20 m/s).
Plugging in these values, KE = (1/2) * 8 * (20^2) = 1600 J.
2. Calculate the final potential energy:
The potential energy at the top of the cliff is equal to the initial kinetic energy. So, the final potential energy (GPE) of the rock just before it hits the ground is also equal to 1600 J.
3. Calculate the height of the cliff:
The gravitational potential energy is given by the formula GPE = m * g * h.
Where m is the mass of the rock (8 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the cliff that we need to find.
Rearranging the formula, h = GPE / (m * g) = 1600 / (8 * 9.8) = 20.4 m.
Therefore, the height of the cliff is 20.4 m.
The correct answer is option C) 20.4 m.