4 of 54 of 5 Items
4 of 54 of 5 Items
Question
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)
Responses
7.5 N
7.5 N
0.01 N
0.01 N
6.5 N
6.5 N
1 N
The force exerted on the ball can be calculated using the formula F = ma, where F is the force, m is the mass of the ball, and a is the acceleration.
First, we need to convert the velocity of the racket from kilometers per hour to meters per second:
65 km/hour = 18.06 m/s
Next, we can use the formula d = 1/2at^2 to find the time it takes for the ball to hit the floor. We know that the initial velocity of the ball is 18.06 m/s and the acceleration is 10 m/s^2. The distance the ball travels is the length of the tennis court, which is typically 23.77 meters for a singles match.
23.77 = 1/2(10)t^2
t^2 = 4.754
t = 2.18 seconds
Now we can use the formula v = at to find the velocity of the ball when it hits the floor.
v = 10 x 2.18 = 21.8 m/s
Finally, we can use the formula F = ma again to find the force exerted on the ball by the floor. The mass of the ball is 0.1 kg and the acceleration is 10 m/s^2.
F = 0.1 x 10 = 1 N
Therefore, the answer is 1 N.
what a lot of work!
As always, F=ma.
Well, it seems like the floor really put its back into it! The force exerted by the floor on the ball is 6.5 N. That's one way to give a ball a good bounce!
To find 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.
Given:
Mass of the tennis ball (m) = 0.1 kg
Acceleration (a) = 10 m/s^2
We need to calculate the force (F).
Using the formula:
F = m * a
Substituting the given values:
F = 0.1 kg * 10 m/s^2
Simplifying the equation:
F = 1 N
Therefore, the force exerted by the floor on the ball is 1 Newton (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).
First, let's convert the velocity of the racket from kilometers per hour to meters per second. Since 1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds, we can use the following conversion:
65 kilometers/hour * (1000 meters/1 kilometer) * (1 hour/3600 seconds) = 18.05 meters/second (rounded to two decimal places).
Next, we can calculate the force exerted by the racket using the formula:
Force = mass * acceleration
Given:
Mass (m) = 0.1 kg
Acceleration (a) = 10 m/s^2
Force = 0.1 kg * 10 m/s^2 = 1 N (Newton)
Therefore, the floor on the south end of the court exerts a force of 1 Newton on the ball.