A person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of vi = 16 m/s. The cliff is h = 60 m above the water's surface, as shown below.
(a) How long does it take for the stone to fall to the water?
s
(b) With what speed does it strike the water?
m/s
To answer these questions, we can use the equations of motion for an object in freefall. Let's break down the problem into two parts:
(a) How long does it take for the stone to fall to the water?
To find the time it takes for the stone to fall, we can use the equation:
h = (1/2) * g * t^2
where h is the height of the cliff (60 m), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time it takes for the stone to fall.
Rearranging the equation to solve for t, we get:
t = sqrt((2 * h) / g)
Plugging in the values, we have:
t = sqrt((2 * 60) / 9.8) = sqrt(12.24) ≈ 3.5 s
Therefore, it takes approximately 3.5 seconds for the stone to fall to the water.
(b) With what speed does it strike the water?
To find the speed, we can use the equation:
v = g * t
where v is the final velocity (speed) of the stone at the time it strikes the water.
Plugging in the values, we have:
v = 9.8 * 3.5 ≈ 34.3 m/s
Therefore, the stone strikes the water with a speed of approximately 34.3 m/s.