Question

A baseball player is running to second base at 5.03 m/s. when he is 4.80 m from the plate he goes into a slide. the coefficient of kinetic friction between the player and the ground is 0.180, and the coefficient of static friction is 3.14. what is his speed when he reaches the plate?

Answer 1

To determine the player's speed when he reaches the plate, we can use the work-energy theorem. Initially, the player is running at a speed of 5.03 m/s. When he slides, the friction between him and the ground slows him down.

Step-by-step explanation:

To determine the player's speed when he reaches the plate, we can use the work-energy theorem. Initially, the player is running at a speed of 5.03 m/s. When he slides, the friction between him and the ground slows him down. The work done by friction can be calculated using the equation Wnc = -fd, where Wnc is the work done by non-conservative forces (in this case, friction), f is the force of friction, and d is the distance over which the force is applied.

We can use the work done by friction to find the change in kinetic energy of the player and then calculate the final speed when he reaches the plate. The work done by friction is negative because it acts in the opposite direction of the motion. The equation simplifies to Wnc = -fd = ΔKE, where ΔKE is the change in kinetic energy.

By setting the work done by friction equal to the change in kinetic energy and solving for the final speed, we can find the player's speed when he reaches the plate.

Answer 2

you can use vf^2 = vi^2 + ad,
where
vf = final velocity,
vi = initial velocity,
a = acceleration,
and
d= distance.
mu = force of friction /force normal, so
force of friction = mu x force normal = mu x weight in this case
force of friction = ma = mu x mg substituting mg for weight
Dividing by m gives you a = mu x g so his acceleration, which is negative because he is slowing, is
-.18(9.8)= 1.764 m/s^2
vf = what you are looking for, so substituting in the first formula, we get
vf^2 = 5.03^2 + 2(-.18)(9.8)(4.8) Take the square root of both sides, and you have it.
vf= 2.89 m/s.