A high diver of mass 52 kg jumps off a board 11 m above the water. If, 4.7 s after entering the water his downward motion is stopped, what average upward force did the water exert?
(average force)*(time underwater) = (momentum change)
The Kinetic Energy entering the water was
KE = M g H = 5606 J
V (entering water) = sqrt(2*KE/m) = 14.7 m/s
Momentum change under water (at lowest depth) = M*V = 764 kg m/s
Now divide by the 4.7 s for the average force in Newtons
162.533N
To find the average upward force exerted by the water, we need to use Newton's second law, which states that force is equal to the rate of change of momentum. In this case, we can determine the force by considering the change in momentum of the high diver.
First, let's calculate the initial velocity of the high diver just before entering the water. We can use the equation for free fall motion:
v = √(2gh)
where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height (11 m in this case).
v = √(2 * 9.8 * 11) ≈ 15.8 m/s (rounded to one decimal place)
Now that we have the initial velocity, we can calculate the final velocity after 4.7 seconds using the equation:
v = u + at
where u is the initial velocity, a is the acceleration (which we assume to be constant), t is the time (4.7s), and v is the final velocity.
The acceleration can be calculated using the following equation:
a = (v - u) / t
a = (0 - 15.8) / 4.7 ≈ -3.4 m/s² (rounded to one decimal place)
Note that the acceleration is negative because it is in the opposite direction of the initial velocity.
Now that we have the acceleration, we can calculate the change in momentum using:
Δp = m * Δv
where Δp is the change in momentum, m is the mass of the diver (52 kg), and Δv is the change in velocity.
Δp = m * Δv = m * (v - u)
Δp = 52 * (0 - 15.8) = -821.6 kg·m/s (rounded to one decimal place)
Since the momentum change is in the downward direction, the average upward force exerted by the water is equal in magnitude but opposite in direction:
F = Δp / t = -821.6 / 4.7 ≈ -175.0 N (rounded to one decimal place)
Therefore, the average upward force exerted by the water is approximately 175.0 Newtons.