A 42.4 kg diver free falls from the diving board and hits the water with a speed of 14.1 m/s. Based on this information, the height of the tower is
To find the height of the tower, we can use the equation for free fall:
h = (1/2)gt^2
where h is the height of the tower, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time it takes for the diver to fall.
We can find t by using the equation for final velocity:
v = u + gt
where v is the final velocity (14.1 m/s), u is the initial velocity (0 m/s, since the diver starts from rest), and g is the acceleration due to gravity.
Rearranging the formula for t gives us:
t = (v - u) / g
Substituting the given values, we have:
t = (14.1 m/s - 0) / 9.8 m/s^2
t ≈ 1.44 s
Now we can substitute the value of t into the equation for h:
h = (1/2) * 9.8 m/s^2 * (1.44 s)^2
h ≈ 9.84 m
Therefore, the height of the tower is approximately 9.84 meters.