Question

"For his deceit and trickery, Sisyphus was punished by the gods to push a boulder up a hill for all

eternity. When he reached the top, the boulder would roll back down the hill, and Sisyphus was
forced to start all over again. If the hill has a height of 57 m, with an incline of 65°, how long
does it take for the boulder to reach the bottom of the hill? Assume that while he pushes the
boulder up the hill he is traveling westward."
How long does it take for the boulder to reach the bottom of the hill?
A) 2.5 seconds
B) 4.3 seconds
C) 6.1 seconds
D) 8.9 seconds

Answer 1

To calculate the time it takes for the boulder to reach the bottom of the hill, we can use the formula for the final velocity of an object rolling down an inclined plane. The final velocity can be found using the formula v = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the hill. Once we have the final velocity, we can use the equation t = d/v to find the time it takes for the boulder to reach the bottom of the hill.

Step-by-step explanation:

To calculate the time it takes for the boulder to reach the bottom of the hill, we need to find its final velocity. The formula for the final velocity of an object rolling down an inclined plane is v = sqrt(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height of the hill (57 m).

Using this formula, we can calculate the final velocity as follows:

v = sqrt(2 * 9.8 m/s² * 57 m) = 34.8 m/s

Next, we can find the time it takes for the boulder to reach the bottom of the hill using the equation t = d/v, where d is the distance traveled and v is the final velocity. Since the boulder is traveling westward, the distance traveled is equal to the length of the hill, which is 57 m.

Using this equation, we can calculate the time as follows:

t = 57 m / 34.8 m/s = 1.64 s

Therefore, it takes approximately 1.64 seconds for the boulder to reach the bottom of the hill.