A 25 kg ball is moving southward at 30 m/s collides with a 10 kg ball moving along the same line with a velocity of 15 m/s southward. After the
collision, the 25 kg ball attains a velocity of 22 m/s southward. What is the velocity of the 10 kg ball?
A. -48.5 m/s
B. 48.7 m/s
C. 47.5 m/s
D. -47.5 m/s
initial momentum South = 25 * 30 + 10 * 15
final momentum south = 25 * 22 + 10 * whatever
so
10* whatever = 750 + 150 - 550 = 350
whatever = 35 m/s
I disagree with all of them
To solve this problem, 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.
The formula for momentum is: momentum = mass * velocity.
Let's denote the velocity of the 10 kg ball as v.
The momentum of the 25 kg ball before the collision is:
momentum1 = mass1 * velocity1 = 25 kg * 30 m/s = 750 kg*m/s.
The momentum of the 10 kg ball before the collision is:
momentum2 = mass2 * velocity2 = 10 kg * 15 m/s = 150 kg*m/s.
The total momentum before the collision is:
total momentum before = momentum1 + momentum2 = 750 kg*m/s + 150 kg*m/s = 900 kg*m/s.
After the collision, the 25 kg ball attains a velocity of 22 m/s southward. Therefore, its momentum after the collision is:
momentum1' = mass1 * velocity1' = 25 kg * 22 m/s = 550 kg*m/s.
The total momentum after the collision is:
total momentum after = momentum1' + momentum2 = 550 kg*m/s + 150 kg*m/s = 700 kg*m/s.
According to the conservation of momentum principle, the total momentum before the collision (900 kg*m/s) is equal to the total momentum after the collision (700 kg*m/s).
Hence, we have the equation:
900 kg*m/s = 700 kg*m/s
Now, we can solve for the velocity of the 10 kg ball (v).
total momentum before = total momentum after
900 kg*m/s = (10 kg * v) + 150 kg*m/s
Simplifying this equation:
900 kg*m/s - 150 kg*m/s = 10 kg * v
750 kg*m/s = 10 kg * v
To find the velocity of the 10 kg ball after 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.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's represent the mass of the 25 kg ball as M1, the velocity of the 25 kg ball before the collision as V1, the mass of the 10 kg ball as M2, the velocity of the 10 kg ball before the collision as V2, and the velocity of the 25 kg ball after the collision as V1f.
Before the collision:
Total momentum = (M1 * V1) + (M2 * V2)
After the collision:
Total momentum = (M1 * V1f) + (M2 * V2f)
Since the collision is along the same line, we can assume that the direction of velocity is negative when moving southward. Therefore, negative values should be used for the velocities pointing southward.
Now we can plug in the known values:
M1 = 25 kg
V1 = -30 m/s
M2 = 10 kg
V2 = -15 m/s
V1f = -22 m/s
Before the collision, the total momentum is:
(25 kg * -30 m/s) + (10 kg * -15 m/s) = -750 kg*m/s + (-150 kg*m/s) = -900 kg*m/s
After the collision, the total momentum is:
(25 kg * -22 m/s) + (10 kg * V2f)
We can now solve for V2f:
V2f = (M1 * V1f + M2 * V2 - (25 kg * -22 m/s)) / 10 kg
Plugging in the values:
V2f = (25 kg * -22 m/s + 10 kg * -15 m/s - (25 kg * -22 m/s)) / 10 kg
V2f = (550 kg*m/s - 150 kg*m/s + 550 kg*m/s) / 10 kg
V2f = 950 kg*m/s / 10 kg
V2f = 95 m/s
Since the velocity is pointing southward, the answer is -95 m/s. Therefore, the velocity of the 10 kg ball after the collision is -95 m/s.
So, the correct answer is:
D. -47.5 m/s