a person standing at the edge of a seaside cliff kicks a stone over the edge with a speed of 10 m/s. the cliff is 48 m above the water's surface as shown. how long does it take for the stone to fall to the water? the acceleration of gravity is 9.81 m/s2. answer in units of s
h = 0.5g*t^2 = 48m. Solve for t.
To find the time it takes for the stone to fall to the water, we can use the kinematic equation:
h = (1/2) * g * t^2
Where:
h = height or distance fallen (48 m)
g = acceleration due to gravity (9.81 m/s^2)
t = time
To solve for t, we rearrange the equation:
t^2 = (2h) / g
Now substitute the given values:
t^2 = (2 * 48 m) / 9.81 m/s^2
t^2 = 96 m / 9.81 m/s^2
t^2 = 9.804 s^2
Taking the square root of both sides:
t = sqrt(9.804 s^2)
t ≈ 3.13 s
Therefore, it takes approximately 3.13 seconds for the stone to fall to the water's surface.