How Is Impulse Calculated in Soccer Ball Deflection?

• physicsgrouch
In summary, there has been concern about heading in youth soccer, and a recent study looked at a player heading a 0.421 kg ball at a 50 degree angle with a constant speed of 10.40m/s. The magnitude of the impulse the player must impart to the ball can be calculated using the equation impulse = m(v_f - v_i). After plugging in the values, the solution is approximately 8.67976478. It was discovered that the wrong angle was being measured, so the correct angle should have been 130 degrees or the x-components of both vectors should have had the same signs.
physicsgrouch
[SOLVED] Impulse of deflected ball

1. Recent studies have raised concern about heading' in youth soccer (i.e., hitting the ball with the head). A soccer player heads' a 0.421 kg ball, deflecting it by 50.0 degrees, and keeps its speed of 10.40m/s constant. (The deflection angle is the angle between the ball's initial and final velocity vectors.) What is the magnitude of the impulse which the player must impart to the ball?

m = 0.421 kg
v$$_{}i$$ = -10.4 m/s
v$$_{}f$$ = 10.4 m/s at 50 degrees

2. The equations

impulse = $$\Delta$$p = m(v$$_{}i$$) - m(v$$_{}f$$)

so impulse = m(v$$_{}f$$ - v$$_{}i$$)

So I multiplied the mass by the change in velocity. Namely:

3. The solution

0.421 *{sqrt[ (10.40*sin50)^2 + (10.40*(cos50 +1))^2) ]}

So I got about 7.936. But this is wrong. What's up?

I think you typed it into the calculator wrong. I just plugged it into google and got
Code:
.421 * sqrt(((10.40 * sin(50))^2) + ((10.40 * (cos(50) + 1))^2)) = 8.67976478

or, in $$\LaTeX$$

$$.421 \sqrt{ \left(10.4\sin{50}\right)^2 + \left(10.4\left(\cos{50}+1\right)\right)^2 } = 8.67976478$$

I think that might be in radians...

Thanks, though. My teacher went over the homework, and it seems that I was measuring the wrong angle. The angle is SUPPOSED to be between the tails of the two vectors, but I was measuring the angle between the tip of the initial and the tail of the final. So my calculations should have treated the angle as 130 degrees. Alternatively, I could have made both vectors' x-components have the same signs.

Thanks anyway.

1. What is impulse of a deflected ball?

Impulse of a deflected ball refers to the change in momentum of the ball as a result of it being deflected or bounced off of a surface.

2. How is impulse of a deflected ball calculated?

The impulse of a deflected ball can be calculated using the formula: impulse = force x time, where force is the force applied to the ball during the deflection and time is the duration of the deflection.

3. What factors affect the impulse of a deflected ball?

The impulse of a deflected ball is affected by the force of the impact, the angle of deflection, the stiffness of the surface, and the elasticity of the ball.

4. How does the impulse of a deflected ball affect its trajectory?

The impulse of a deflected ball can change the direction and speed of the ball's trajectory, depending on the angle and force of the deflection. A greater impulse will result in a greater change in trajectory.

5. Why is understanding the impulse of a deflected ball important?

Understanding the impulse of a deflected ball is important in many sports and activities, as it can help predict the trajectory of the ball and improve performance. It is also important in analyzing the force and impact of collisions in physics and engineering.

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