When taking a penalty kick a footballer applies a force of 30N for a period of 0.05s if the mass of the ball is 0.075kg, calculate the speed with the ball moves off.
To calculate the speed with which the ball moves off, we can use the formula:
Force (F) = Mass (m) x Acceleration (a)
Rearranging the formula to solve for acceleration:
Acceleration (a) = Force (F) / Mass (m)
Plugging in the given values into the equation:
Acceleration (a) = 30 N / 0.075 kg
Acceleration (a) = 400 m/s^2
Next, we can use the formula:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) x Time (t))
Since the initial velocity (u) is usually assumed to be 0 in a penalty kick, the formula simplifies to:
Final velocity (v) = Acceleration (a) x Time (t)
Plugging in the values:
Final velocity (v) = 400 m/s^2 x 0.05 s
Final velocity (v) = 20 m/s
Therefore, the ball moves off with a speed of 20 meters per second.
To calculate the speed at which the ball moves off during a penalty kick, you can use the principle of conservation of momentum. Momentum is defined as the product of an object's mass and its velocity.
The formula for momentum is:
Momentum = mass × velocity
In this case, the initial momentum of the ball is zero since it is at rest before the kick. After the kick, the momentum of the ball is given by the product of its mass and final velocity.
Since the initial momentum is zero, the final momentum is equal to the impulse applied to the ball during the kick. Impulse is defined as the product of force and time. The equation for impulse is:
Impulse = Force × time
In this problem, the force applied is 30 N and the time is 0.05 seconds. Hence:
Impulse = 30 N × 0.05 s
To find the final velocity, we divide the impulse by the mass of the ball:
Final momentum = Impulse = Force × time
Final momentum = (30 N × 0.05 s)
Final momentum = 1.5 N·s
Final velocity = Final momentum / mass
Final velocity = 1.5 N·s / 0.075 kg
Calculating this:
Final velocity = 20 m/s
Therefore, the ball moves off at a speed of 20 m/s during the penalty kick.
Answer
force = mass * change in velocity / change in time
so
force * change in time = mass * change in velocity
which by the way is change of momentum
so
30 N * 0.05 s = 0.075 kg * speed at end
solve for speed at end