A soccer ball with mass 0.410 kg is initially moving with speed 4.30 m/s. A soccer player kicks the ball, exerting a constant force of magnitude 44.0 N in the same direction as the ball's motion. Over what distance must the player's foot be in contact with the ball to increase the ball's speed to 6.70 m/s?
force(time)=change in momentum=mass(Vf-Vi)
force(time)=change in momentum=mass(Vf-Vi)
That gives you the time of contact. The average velocity is Vf+Vi /2, so distance=avg velocity*time.
i still don't understand
A sled with a mass of 9.50 kg moves in a straight line on a frictionless horizontal surface. At one point in its path, its speed is 2.80 m/s; after it has traveled 2.50 m beyond this point, its speed is 6.50 m/s. Use the work-energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion.
To solve this problem, we can use the concept of work and energy. The work done on an object is equal to the change in its kinetic energy.
1. First, let's find the initial kinetic energy (KEi) of the soccer ball. We can use the formula:
KEi = 0.5 * mass * velocity^2
Plugging in the values:
KEi = 0.5 * 0.410 kg * (4.30 m/s)^2
= 4.592 J (Joules)
2. Next, let's find the final kinetic energy (KEf) of the soccer ball. We can use the same formula with the final velocity:
KEf = 0.5 * mass * velocity^2
Plugging in the values:
KEf = 0.5 * 0.410 kg * (6.70 m/s)^2
= 7.241 J (Joules)
3. The change in kinetic energy (ΔKE) is given by the difference between the final and initial kinetic energy:
ΔKE = KEf - KEi
= 7.241 J - 4.592 J
= 2.649 J (Joules)
4. The work done (W) on the ball is equal to the change in kinetic energy:
W = ΔKE
5. The work done (W) can also be calculated by multiplying the force (F) applied by the player with the distance (d) over which the force is applied:
W = F * d
So, we have F * d = ΔKE.
6. Rearranging the equation to solve for distance (d):
d = ΔKE / F
Plugging in the values:
d = 2.649 J / 44.0 N
≈ 0.060 m or 6.0 cm
Therefore, the player's foot must be in contact with the ball for a distance of approximately 0.060 meters or 6.0 centimeters to increase the ball's speed to 6.70 m/s.