A barefoot field-goal kicker imparts a speed

of 33 m/s to a football initially at rest.
If the football has a mass of 0.75 kg and the
time of contact with the ball is 0.015 s, what
is the force exerted by the ball on the kicker’s
foot?

To find the force exerted by the ball on the kicker's foot, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

F = m * a

In this case, the mass of the football is 0.75 kg, and the football starts from rest and reaches a final speed of 33 m/s. We can calculate the acceleration as the change in velocity divided by the time taken:

a = (final velocity - initial velocity) / time

a = (33 m/s - 0) / 0.015 s

a = 33 m/s / 0.015 s

a = 2200 m/s²

Now, we can substitute the values of mass (m) and acceleration (a) into Newton's second law to find the force:

F = 0.75 kg * 2200 m/s²

F = 1650 N

Therefore, the force exerted by the ball on the kicker's foot is 1650 Newtons.

To find the force exerted by the ball on the kicker's foot, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum. The momentum of an object is calculated by multiplying its mass by its velocity.

The formula for momentum is:
Momentum (p) = mass (m) × velocity (v)

In this case, the initial velocity of the football is 0 m/s, and it is kicked with a speed of 33 m/s. The mass of the football is given as 0.75 kg.

So, the change in momentum of the football can be calculated as:
Change in momentum (Δp) = (mass of the football) × (final velocity of the football - initial velocity of the football)
= 0.75 kg × (33 m/s - 0 m/s)
= 0.75 kg × 33 m/s

Now, we need to find the force exerted by the football on the kicker's foot during the 0.015 seconds of contact. The force can be calculated using the formula:
Force (F) = change in momentum (Δp) / time (t)

Substituting the values we have:
Force (F) = (0.75 kg × 33 m/s) / 0.015 s

Simplifying the equation will give us the answer.

Calculating the result: