A tennis player hits a 0.1-kilogram tennis ball with her racket from the north end of a court. Her racket was traveling at 65 kilometers per hour. The ball accelerated at a rate of 10 meters per second squared. The ball hits the floor on the south end of the tennis court. The floor sends the ball toward the tennis player's opponent with the same acceleration. How much force did the floor on the south end of the court exert on the ball?
A. 7.5 N
B. 1N
C. 0.01 N
D. 6.5 N
To solve this problem, we can use Newton's second law, which states that force (F) is equal to mass (m) times acceleration (a).
First, we need to convert the velocity of the racket from kilometers per hour to meters per second. We can do this by dividing 65 kilometers per hour by 3.6:
65 km/h ÷ 3.6 = 18.055... m/s
Next, we can calculate the initial force exerted by the racket on the ball using the formula F = m x a:
F = 0.1 kg x 18.055... m/s^2 = 1.8055... N
Since the floor exerts an equal force on the ball as it hits the south end of the court, the force exerted by the floor on the ball is also 1.8055... N.
Therefore, the correct answer is closest to D. 6.5 N.
To determine the force exerted by the floor on the ball, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
Step 1: Convert the velocity of the racket from kilometers per hour to meters per second.
The racket was traveling at 65 kilometers per hour, so we need to convert this to meters per second.
Since 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds, we can calculate the velocity in meters per second as follows:
65 kilometers per hour = (65 x 1000) meters / (3600 seconds) ≈ 18.06 m/s
Step 2: Calculate the force exerted by the racket on the ball.
The mass of the ball is given as 0.1 kilograms, and the acceleration of the ball is given as 10 meters per second squared. Using Newton's second law, we can calculate the force exerted by the racket as follows:
Force = mass x acceleration
Force = 0.1 kg x 10 m/s^2 = 1 N
Step 3: Since the floor sends the ball toward the tennis player's opponent with the same acceleration, the force exerted by the floor on the ball will also be 1 N.
Therefore, the correct answer is B. 1 N.
To find the force exerted by the floor on the ball, we need to use Newton's second law of motion:
F = m * a
where:
F is the force
m is the mass of the ball
a is the acceleration of the ball
First, we need to convert the mass of the ball from kilograms to grams, since the unit for acceleration is in meters per second squared.
1 kilogram = 1000 grams
So, the mass of the ball in grams is 0.1 * 1000 = 100 grams.
Next, we need to convert the acceleration from meters per second squared to kilometers per hour squared.
1 meter = 0.001 kilometers
1 second = 3600 seconds (1 hour)
So, the acceleration of the ball in kilometers per hour squared is:
10 * (0.001 / (3600^2)) = 0.00000007716 kilometers per hour squared.
Now, we can substitute the values into the formula:
F = 0.1 kg * 0.00000007716 km/hr^2
To get the force in Newtons, we need to convert the mass from grams back to kilograms:
0.1 kg = 100 grams
F = 100 grams * 0.00000007716 km/hr^2
Finally, we convert the answer from kg * km/hr^2 to Newtons by dividing by 1000:
F = (100 grams * 0.00000007716 km/hr^2) / 1000 = 0.0000007716 N
Therefore, the force exerted by the floor on the ball is approximately 0.0000007716 N.
The closest option to this answer is C. 0.01 N.