Tennis Ball: Force, Weight, G-Force & Acceleration at 200 km/h

[t1000ct]

Homework Statement

When served at 200 km/h (124 mph), what is the equivalent weight exerted on the tennis ball?

15 kg
162 kg
200 kg
320 kg

How much G-Force must a tennis ball sustain when served at 200 km/h (124 mph)? (for example the G-Force when flying a jet = 8G)

3G
50G
220G
1400G

How fast does a tennis ball accelerate from 0-100 km/h (62 mph) when serving at 200 km/h (124 mph)?

2.5 sec
3/10 sec
7/100 sec
4/1000 sec

Mass of a tennis ball = 56-59.6 grams so I used the mid point (57 grams)
200 km/h = 55 m/s
distance covered by the tennis ball is 0.6096 meters

Homework Equations

f=ma
a = change in time x change in velocity
Don't know what to use for 3, formula for distance?

The Attempt at a Solution

(1) I thought that the speed given is velocity and found it to be 5063.799 m/s
Force = 288.64 N and the weight exerted = 29.433 kg, which isn't any of the answers

also did 55.56(.057) = 3.692 N and it doesn't match any of the answers

(2) I just did f=ma and got 3.2 and i thought that this was the answer since it is close to 3G but I'm not sure if I'm right or not

(3) I honestly have no idea how to do this. I took Honors Physics as a Junior in HS and now I'm a freshman in college and I don't remember any of this.

Thanks!

 

[anathema]

Hello!

To solve this problem, we need to use the equations of motion, specifically the one that relates acceleration, initial velocity, final velocity, and time:

v = u + at

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

For the first part of the problem, we need to find the weight exerted on the tennis ball when served at 200 km/h. The weight exerted is the same as the force acting on the ball, so we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

Using the given information, we can find the acceleration by rearranging the equation above:

a = (v-u)/t

Where:
v = final velocity = 200 km/h = 55.56 m/s
u = initial velocity = 0 m/s
t = time = 0.6096/55.56 = 0.010986 seconds

Plugging these values into the equation, we get:

a = (55.56-0)/0.010986 = 5063.799 m/s^2

Now, we can plug this value into the formula F = ma to find the force:

F = (0.057 kg)(5063.799 m/s^2) = 291.65 N

This is the force exerted on the tennis ball when served at 200 km/h. However, the question asks for the weight exerted, which is equal to the force divided by the acceleration due to gravity (9.8 m/s^2). So, the weight exerted on the tennis ball is:

W = 291.65 N / 9.8 m/s^2 = 29.73 kg

Since this value is closest to 30 kg, the correct answer is 29.73 kg.

For the second part of the problem, we need to find the G-Force experienced by the tennis ball when served at 200 km/h. G-Force is a measure of acceleration, so we can use the same formula as before to find the acceleration:

a = (55.56-0)/0.010986 = 5063.799 m/s^2

To find the G-Force, we need to divide this value by the acceleration due to gravity:

G-Force = 5063.799 m/s^2 / 9.