During a football match, the ball shot towards the goal struck the defender's foot at the speed of 10m/s and it bounced back at 20m/s. If the time of impact was 0.2 sec, and mass of the ball 0.5 kg,then find the average force exerted by defender on the ball.

a = Vf-Vo)/t,

a = (--20-10) / 0.2 = -150 m/s^2 in
opposite direction.

F = ma = 0.5 * (-150) = -75 N. = opposing force.

Well, it seems like the defender took one for the team! Let's calculate the average force he exerted on the ball.

We need to use Newton's second law, which states that force (F) equals mass (m) times acceleration (a). Since we're given the time of impact, we can calculate the acceleration using the formula a = (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time.

Here's the math:

Initial velocity (u) = 10 m/s
Final velocity (v) = -20 m/s (negative because it bounced back)
Time (t) = 0.2 s

Acceleration (a) = (v - u) / t
= (-20 - 10) / 0.2
= -30 / 0.2
= -150 m/s²

Using the equation F = m * a, we can now calculate the average force.

Mass (m) = 0.5 kg
Acceleration (a) = -150 m/s²

Average force (F) = m * a
= 0.5 kg * -150 m/s²
= -75 N

So, the average force exerted by the defender on the ball is -75 Newtons. Don't worry, he was just trying to make the ball bounce back, not take it out to dinner!

To find the average force exerted by the defender on the ball, we can use the equation:

Average force = change in momentum / time

First, let's calculate the initial momentum (pi) of the ball:

pi = mass x initial velocity
= 0.5 kg x 10 m/s
= 5 kg·m/s

Next, let's calculate the final momentum (pf) of the ball:

pf = mass x final velocity
= 0.5 kg x (-20 m/s) (since the velocity is in the opposite direction)
= -10 kg·m/s

The change in momentum (Δp) is the difference between the final and initial momentum:

Δp = pf - pi
= (-10 kg·m/s) - (5 kg·m/s)
= -15 kg·m/s

Finally, we can calculate the average force exerted by the defender on the ball using the given time of impact:

Average force = Δp / time
= (-15 kg·m/s) / (0.2 s)
= -75 kg·m/s²

Therefore, the average force exerted by the defender on the ball is -75 kg·m/s²

To find the average force exerted by the defender on the ball, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (p) with respect to time (t).

The momentum of an object can be calculated by multiplying its mass (m) by its velocity (v). Therefore, the initial momentum of the ball before impact is given by p1 = m * v1, and the final momentum after impact is given by p2 = m * v2.

The rate of change of momentum (Δp) can then be calculated by subtracting the initial momentum from the final momentum: Δp = p2 - p1.

Since the force on the ball acts for a time duration (Δt) of 0.2 s, the average force (F) can be calculated by dividing the change in momentum by the time: F = Δp / Δt.

Now, let's substitute the given values into the equations:

Initial momentum (p1) = m * v1 = 0.5 kg * 10 m/s = 5 kg * m/s
Final momentum (p2) = m * v2 = 0.5 kg * 20 m/s = 10 kg * m/s
Change in momentum (Δp) = p2 - p1 = 10 kg * m/s - 5 kg * m/s = 5 kg * m/s
Time duration (Δt) = 0.2 s

Now, we can calculate the average force (F):

F = Δp / Δt = 5 kg * m/s / 0.2 s = 25 N

Therefore, the average force exerted by the defender on the ball is 25 Newtons (N).