To determine the force exerted by the floor on the south end of the court, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
First, let's calculate the initial velocity of the tennis ball when it hits the floor. We are given that the racket was traveling at 65 kilometers per hour. To convert this to meters per second, we divide by 3.6 (because 1 kilometer per hour equals 1 kilometer per 3.6 seconds). Therefore, the initial velocity of the tennis ball is 65 km/h / 3.6 = 18.06 m/s.
Next, we need to calculate the time it takes for the ball to travel from the north end to the south end of the court. In order to find this, we can use the kinematic equation:
v = u + at
where v is the final velocity (0 m/s), u is the initial velocity (18.06 m/s), a is the acceleration (-10 m/s^2), and t is the time.
Rearranging the equation to solve for t:
t = (v - u) / a
t = (0 - 18.06) / -10
t ≈ 1.806 seconds
Now let's calculate the distance traveled by the ball. We can use the formula:
s = ut + (1/2)at^2
where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.
s = 18.06 * 1.806 + (1/2)(-10)(1.806)^2
s ≈ 16.39 meters
Finally, we can calculate the force exerted by the floor by multiplying the mass of the ball (0.1 kg) by the acceleration (10 m/s^2). This gives us:
F = m * a
F = 0.1 * 10
F = 1 N
Therefore, the answer is 1 N.
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