A baseball player with a mass of 79 kg slides into homeplate. The coefficient of kinetic friction between the player and the ground is μk = 0.632. If the player comes to rest after 1.04 s, what is his initial speed?
To find the initial speed of the baseball player, we can use the equation:
v = u + at
Where:
- v represents the final velocity (which is zero since the player comes to rest)
- u represents the initial velocity (what we are trying to find)
- a represents the acceleration
- t represents the time
First, let's calculate the acceleration using the equation:
a = μk * g
Where:
- μk represents the coefficient of kinetic friction
- g represents the acceleration due to gravity (approximately 9.8 m/s²)
Substituting the given values, we get:
a = 0.632 * 9.8
Now, let's calculate the acceleration:
a = 6.1576 m/s²
We can now substitute the values of a, v, and t into the equation v = u + at:
0 = u + 6.1576 * 1.04
Simplifying, we have:
0 = u + 6.394304
Now, isolate u by subtracting 6.394304 from both sides of the equation:
u = -6.394304
Since velocity is a vector quantity, the negative sign indicates that the initial velocity is in the opposite direction of motion. Therefore, the initial speed of the player is approximately 6.39 m/s, directed opposite to the motion.