two basketball players collide player 1 with a mass of 55.0 kg experiences a -15.6 m/s2 acceleration. if the player 2 has a mass of 48.5 kg what acceleration did he experience immediately following the collision?
the two players experience equal but opposite impulses from the collision
M1 * A1 = M2 * A2
To find the acceleration experienced by player 2 immediately following the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces.
The formula for momentum is:
momentum = mass × velocity
Let's denote player 1's velocity before the collision as v1 and player 2's velocity before the collision as v2. Since the players collide, their velocities will change.
Before the collision:
Player 1's momentum = mass 1 × velocity 1 = 55.0 kg × v1
Player 2's momentum = mass 2 × velocity 2 = 48.5 kg × v2
After the collision:
Player 1's momentum = mass 1 × velocity 1' (where velocity 1' is the final velocity of player 1)
Player 2's momentum = mass 2 × velocity 2' (where velocity 2' is the final velocity of player 2)
According to the conservation of momentum:
Initial total momentum = Final total momentum
Initial total momentum = Player 1's momentum + Player 2's momentum
Final total momentum = Player 1's momentum + Player 2's momentum
Therefore,
mass 1 × velocity 1 + mass 2 × velocity 2 = mass 1 × velocity 1' + mass 2 × velocity 2'
Rearranging the equation, we get:
mass 1 × (velocity 1 - velocity 1') = mass 2 × (velocity 2' - velocity 2)
Now let's substitute the given values:
mass 1 = 55.0 kg
velocity 1 = 0 m/s (assuming player 1 is stationary)
velocity 1' = -15.6 m/s^2 (given negative acceleration)
mass 2 = 48.5 kg
velocity 2 = ? (unknown)
velocity 2' = ? (unknown)
By plugging in these values, the equation becomes:
55.0 kg × (0 - (-15.6 m/s^2)) = 48.5 kg × (velocity 2' - velocity 2)
Simplifying, we have:
55.0 kg × 15.6 m/s^2 = 48.5 kg × (velocity 2' - velocity 2)
Now solve for velocity 2' - velocity 2:
velocity 2' - velocity 2 = (55.0 kg × 15.6 m/s^2) / 48.5 kg
Finally, divide both sides by 48.5 kg to solve for velocity 2':
velocity 2' = (55.0 kg × 15.6 m/s^2) / 48.5 kg + velocity 2
Once you have the value of velocity 2', you can subtract the initial velocity (velocity 2) to find the acceleration experienced by player 2 immediately following the collision.