Final answer:
The height of the cliff from which the rock was thrown is calculated using the equations of motion, considering initial velocity and acceleration due to gravity. After solving the equation, the height is found to be approximately 21.12 meters.
Step-by-step explanation:
To calculate the height of the cliff from which a rock is thrown straight up with an initial velocity of 8.1 m/s and takes 3.05 s to hit the ground, we can use the equations of motion under constant acceleration due to gravity. The equation that relates time, initial velocity, acceleration, and displacement is:
s = ut + 1/2 at2
Where:
- s is the displacement (height of the cliff)
- u is the initial velocity (8.1 m/s upward)
- a is the acceleration due to gravity (9.81 m/s2, downward)
- t is the time taken to reach the ground (3.05 s)
Since the rock is thrown upwards, the initial velocity is positive, but the acceleration due to gravity is negative because it is in the opposite direction:
s = (8.1 m/s)(3.05 s) + 1/2 (-9.81 m/s2)(3.05 s)2
Upon calculation:
s = 24.705 - 45.820725
s = -21.115725 m
The negative sign indicates that the point of reference (top of the cliff) is above the landing point (ground). Therefore, the height of the cliff is 21.115725 meters, when rounded, approximately 21.12 meters.