Question

Cliff divers at Acapulco jump into the sea from a cliff 34.8 m high. At the level of the sea, a rock sticks out a horizontal distance of 11.37 m. The acceleration of gravity is 9.8 m/s². With what minimum horizontal velocity must the cliff divers leave the top of the cliff if they are to miss the rock?

Answer 1

To miss the rock, the cliff divers must leave the top of the cliff with a minimum horizontal velocity of 5.53 m/s.

Step-by-step explanation:

To calculate the minimum horizontal velocity a cliff diver must leave the top of the cliff with in order to miss a rock, we can use the equation for horizontal distance:

d = v0 * t

where d is the horizontal distance, v0 is the initial velocity, and t is the time.

In this case, the initial vertical velocity is 0 because the cliff diver jumps horizontally. Therefore, the time it takes for the cliff diver to hit the water is the same as the time it takes for the rock to hit the ground when thrown vertically upward. Using the equation for time:

t = sqrt((2h) / g)

where h is the height and g is the acceleration due to gravity, we can calculate the time as:

t = sqrt((2 * 34.8) / 9.8) = 2.05 s

Substituting this value into the equation for horizontal distance, we can solve for the initial velocity:

11.37 = v0 * 2.05

v0 = 5.53 m/s

Therefore, the minimum horizontal velocity the cliff divers must leave the top of the cliff with is 5.53 m/s in order to miss the rock.