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?
(1 point)
A.) 7.5 N
B.) 1 N
C.) 0.01 N
D.) 6.5 N
To solve this problem, we can use Newton's second law, which states that force equals mass times acceleration (F = ma).
First, we need to convert the racket's velocity from kilometers per hour to meters per second. We know that 1 kilometer equals 1000 meters and 1 hour equals 3600 seconds. Therefore, the racket's velocity is:
65 kilometers per hour = (65 * 1000 meters) / (3600 seconds) = 18.06 meters per second
Next, we can calculate the force exerted by the racket on the ball. We know the ball's mass (0.1 kilograms) and the racket's acceleration (which is equivalent to the ball's acceleration, since they have the same value). Using Newton's second law, we have:
Force = mass * acceleration = 0.1 kg * 10 m/s^2 = 1 N
So, the force exerted by the racket on the ball is 1 Newton.
Finally, we can determine the force exerted by the floor on the ball. Since the floor sends the ball towards the tennis player's opponent with the same acceleration, the force exerted by the floor is equal in magnitude to the force exerted by the racket, which is 1 Newton.
Therefore, the correct answer is B.) 1 N.
To find the force exerted by the floor on the ball, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
Given:
Mass of the tennis ball (m) = 0.1 kg
Acceleration of the ball (a) = 10 m/s^2
Using Newton's second law of motion, we can calculate the force exerted by the floor on the ball:
F = m * a
F = 0.1 kg * 10 m/s^2
F = 1 N
Therefore, the force exerted by the floor on the ball is 1 N.
The correct answer is B.) 1 N.
To find the force exerted by the floor on the south end of the court on the tennis ball, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
1. Convert the mass of the tennis ball from kilograms to grams. There are 1000 grams in 1 kilogram, so the mass of the tennis ball is 100 grams.
2. Convert the speed of the racket from kilometers per hour to meters per second. Since there are 1000 meters in 1 kilometer and 3600 seconds in 1 hour, the speed of the racket is 65,000/3600 = 18.06 m/s.
3. Apply the formula for acceleration: a = (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time taken. Rearrange the formula to solve for time (t): t = (v - u) / a. Since the ball was hit from the north end of the court, its initial velocity is 0 m/s, and the final velocity is unknown. However, the final velocity can be determined using the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. In this case, the displacement is the length of the tennis court, which is not provided in the question. Therefore, it is not possible to calculate the final velocity and the time taken accurately.
4. Since the final velocity and time taken cannot be accurately calculated, we cannot directly calculate the force exerted by the floor on the south end of the court on the tennis ball. Therefore, we cannot determine the correct answer from the options provided (A, B, C, D).