# Finding the Speed of a head hit by a soccer ball

• HappyFlower
In summary, the acceleration of a soccer player's head when heading a ball can be significant, as shown in Figure 2-38. At time t = 7.0 ms, the difference in speed acquired by a bare head and a helmeted head is approximately 0.56 m/s, calculated by finding the area under each curve. However, the graph may not accurately represent the true benefits of wearing a helmet, as it may only spread the impulse over a longer duration rather than reducing its magnitude.
HappyFlower

## Homework Statement

When a soccer ball is kicked toward a player and the player deflects the ball by "heading" it, the acceleration of the head during the collision can be significant. Figure 2-38 gives the measured acceleration a(t) of a soccer player's head for a bare head and a helmeted head, starting from rest. At time t = 7 .0 ms, what is the difference in the speed acquired by the bare head and the speed acquired by the helmetedhead?

## The Attempt at a Solution

I uploaded the picture of the graph and question also I was able to get an answer. I found the peak of the helmet graph to be 80 m/s^2 and .006s. I found the other peak from the bare graph to be 200 m/s^2 and .006s.
I multiplied 80 m/s^2 * .006s=.48 m/s and 200 m/s^2 *.006s =1.2 m/s
1.2 m/s- .48 m/s =.57 m/s
the answer of the problem is .56 m/s, I was wondering if I did the problem the right way?

#### Attachments

• soccer ball problem.jpg
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The final velocity is the area under each curve v = ∫a dt. You have a whole bunch of triangle and rectangle areas to calculate. Go for it.

As an aside, the graph completely misrepresents reality. The player intends to impart a specific impulse to the ball. If that is being achieved in both graphs then the helmet must be heavier than the head!
The real benefit of the helmet is the extent to which it spreads the impulse over a longer duration.

## 1. How do you measure the speed of a soccer ball hitting someone's head?

To measure the speed of a soccer ball hitting someone's head, you would need to use a speed measuring device such as a radar gun or a high-speed camera. The device should be placed at a fixed distance from the point of impact and calibrated to accurately measure the speed of the ball.

## 2. What factors affect the speed of a soccer ball hitting someone's head?

The speed of a soccer ball hitting someone's head can be affected by various factors such as the initial speed of the ball, the angle of impact, the weight and size of the ball, and the strength and position of the person's head.

## 3. Can the speed of a soccer ball hitting someone's head cause injuries?

Yes, the speed of a soccer ball hitting someone's head can potentially cause injuries, especially if the impact is strong enough. The force of the impact can cause concussions, bruises, or even skull fractures.

## 4. How accurate is the measurement of the speed of a soccer ball hitting someone's head?

The accuracy of the speed measurement depends on the accuracy and precision of the speed measuring device used. It is important to use a reliable and properly calibrated device to get an accurate measurement.

## 5. Are there any safety precautions when conducting experiments to measure the speed of a soccer ball hitting someone's head?

Yes, it is important to take safety precautions when conducting experiments to measure the speed of a soccer ball hitting someone's head. This includes using protective gear such as helmets and safety goggles, choosing a safe and controlled environment, and following proper experimental procedures to minimize the risk of injury.

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