A person standing at the edge of a seaside
cliff kicks a stone over the edge with a speed
of 21 m/s. The cliff is 52 m above the water’s
surface. How long does it take for the stone to fall
to the water? The acceleration of gravity is
9.81 m/s^2.
Thanks!
To find the time it takes for the stone to fall to the water, we can use the formula for the time of flight for an object in free fall:
t = sqrt((2h) / g),
Where:
t = time
h = height
g = acceleration due to gravity
In this case, the height (h) is 52 m and the acceleration due to gravity (g) is 9.81 m/s^2.
Let's substitute the values into the formula:
t = sqrt((2 * 52) / 9.81)
Calculating this equation, we get:
t ≈ sqrt(104 / 9.81)
t ≈ sqrt(10.589757)
t ≈ 3.26 s
Therefore, it takes approximately 3.26 seconds for the stone to fall to the water.
To find the time it takes for the stone to fall to the water, we can use the kinematic equation:
d = v_i * t + (1/2) * a * t^2
where:
d = distance traveled (52 m)
v_i = initial velocity (21 m/s)
a = acceleration (gravity, -9.81 m/s^2) since it acts opposite to the stone's motion
t = time
Rearranging the equation to solve for time:
52 = 21t + (1/2) * (-9.81) * t^2
Now we can solve this quadratic equation.