Question

Divers in Acapulco dive from a cliff running at 2.8 m/s as their projectile takes 1.78 seconds to reach the water below. How high is the cliff? How far away from the base of the cliff does the diver hit the water?

Answer 1

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To find the height of the cliff, we can use the equation:

h = (1/2) * g * t^2

Where:

h is the height of the cliff (unknown)

g is the acceleration due to gravity, approximately 9.8 m/s^2

t is the time taken to reach the water, which is given as 1.78 seconds

Plugging in the values, we get:

h = (1/2) * (9.8 m/s^2) * (1.78 s)^2

h = 15.81 meters

So, the height of the cliff is approximately 15.81 meters.

To find the distance away from the base of the cliff that the diver hits the water, we can use the equation:

d = v * t

Where:

d is the horizontal distance (unknown)

v is the horizontal velocity, which is given as 2.8 m/s

t is the time taken to reach the water, which is given as 1.78 seconds

Plugging in the values, we get:

d = (2.8 m/s) * (1.78 s)

d = 4.984 meters

So, the diver hits the water approximately 4.984 meters away from the base of the cliff.