a tennis ball 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. the ball hits the floor on the south end of the tennis court. how much force did the floor on the south end of the court exert on the ball
To calculate 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:
Force = mass × acceleration
First, we need to convert the speed of the racket from kilometers per hour to meters per second:
65 kilometers/hour = (65 × 1000) meters / (60 × 60) seconds
= 18.06 meters/second (rounded to two decimal places)
Given:
Mass of the tennis ball (m) = 0.1 kg
Acceleration of the ball (a) = 10 m/s²
Using Newton's second law, we can calculate the force:
Force = mass × acceleration
Force = 0.1 kg × 10 m/s²
Force = 1 N
Therefore, the floor on the south end of the court exerts a force of 1 Newton on the tennis ball.
To determine 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 force (F) is equal to mass (m) multiplied by acceleration (a).
Mass of the tennis ball (m) = 0.1 kg
Acceleration of the tennis ball (a) = 10 m/s^2 (assuming the given value is in meters per second squared)
First, let's convert the velocity of the racket from km/h to m/s:
Velocity of the racket = 65 km/h
= 65 × (1000/3600) m/s
= 18.06 m/s
Since the ball is hit by the racket, it inherits the velocity of the racket. Therefore, the initial velocity of the ball is also 18.06 m/s.
Using the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, as the ball hits the floor)
u = initial velocity (18.06 m/s)
a = acceleration (10 m/s^2)
s = displacement (let's assume the displacement to be the length of the court)
Let's solve for the displacement (s):
0^2 = 18.06^2 + 2(10)s
0 = 326.7636 + 20s
20s = -326.7636
s = -16.33818 m
Since the displacement value is negative, it means the ball moves in the opposite direction (from north to south).
Now, let's 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 floor on the south end of the court exerts a force of 1 Newton (N) on the tennis ball.
To determine the force exerted by the floor on the tennis ball, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a).
Given information:
Mass of the tennis ball (m): 0.1 kg
Acceleration of the tennis ball (a): 10 m/s²
To find the force (F), we need to find the final velocity (v) of the tennis ball. We can do this using the kinematic equation:
v² = u² + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
With the given information, the initial velocity (u) is the velocity of the racket and the displacement (s) is the length of the tennis court. However, the initial velocity is given in kilometers per hour (km/h) while the displacement is not provided. For the sake of providing an explanation, let's assume the length of the tennis court is 23 meters.
First, we need to convert the initial velocity from km/h to m/s by dividing it by 3.6 (since 1 km/h = 1000 m/3600 s = 1/3.6 m/s).
Initial velocity (u) = 65 km/h = (65/3.6) m/s ≈ 18.06 m/s
Using the kinematic equation:
v² = u² + 2as
v² = (18.06)² + 2(10)(23)
v² = 326.5236 + 460
v² ≈ 786.5236
v ≈ √786.5236
v ≈ 28.04 m/s (rounded to two decimal places)
Now that we have the final velocity (v), we can calculate the force (F) exerted by the floor on the ball.
F = m * a
F = 0.1 kg * 10 m/s²
F = 1 N
Therefore, the floor on the south end of the court exerts a force of 1 Newton on the tennis ball.