A ball with a mass of 0.50 kilograms is moving at a speed of 1.8 meters/second along the positive x-axis. It collides with another ball of the same mass travelling at a speed of 2.0 meters/second toward the positive y-axis. Both balls then start moving together. What is the magnitude of the resultant momentum before collision?
A. 1.3 kilogram meters/second
B. 1.5 kilogram meters/second
C. 1.8 kilogram meters/second
D. 2.1 kilogram meters/second
Try applying conservation of momentum.
The resultant momentum of both objects (taken together) will be conserved.
sqrt[(0.5*1.8)^2 + (0.5*2.0)^2] = 1.3454 kg m/s
They want you to keep just two significant figures, so use 1.3.
To find the magnitude of the resultant momentum before the collision, we need to calculate the momentum of each ball separately and then sum them up.
The momentum of an object is calculated by multiplying its mass by its velocity:
Momentum = mass × velocity
For the first ball moving along the positive x-axis, its momentum is given by:
Momentum1 = mass1 × velocity1
Momentum1 = 0.50 kg × 1.8 m/s
Momentum1 = 0.90 kg·m/s
For the second ball moving toward the positive y-axis, its momentum is given by:
Momentum2 = mass2 × velocity2
Momentum2 = 0.50 kg × 2.0 m/s
Momentum2 = 1.00 kg·m/s
Now, finding the magnitude of the resultant momentum:
Resultant Momentum = √ ((Momentum1)^2 + (Momentum2)^2)
Resultant Momentum = √ ((0.90 kg·m/s)^2 + (1.00 kg·m/s)^2)
Resultant Momentum ≈ √ ((0.81 kg^2·m^2/s^2) + (1.00 kg^2·m^2/s^2))
Resultant Momentum ≈ √ (1.81 kg^2·m^2/s^2)
Resultant Momentum ≈ 1.35 kg·m/s
Therefore, the magnitude of the resultant momentum before collision is approximately 1.35 kilogram meters/second.
The closest option to this value is:
B. 1.5 kilogram meters/second
To find the magnitude of the resultant momentum before the collision, we need to calculate the individual momenta of the two balls and then add them together.
The momentum of an object is given by the product of its mass and velocity. The formula for momentum is:
Momentum = mass × velocity
For the first ball:
Mass of ball 1 = 0.50 kg
Velocity of ball 1 along the positive x-axis = 1.8 meters/second
Using the formula, we can calculate the momentum of ball 1:
Momentum of ball 1 = 0.50 kg × 1.8 m/s = 0.90 kg m/s
For the second ball:
Mass of ball 2 = 0.50 kg
Velocity of ball 2 along the positive y-axis = 2.0 meters/second
Using the formula, we can calculate the momentum of ball 2:
Momentum of ball 2 = 0.50 kg × 2.0 m/s = 1.00 kg m/s
Now, to find the magnitude of the resultant momentum before the collision, we add the individual momenta:
Resultant momentum = Momentum of ball 1 + Momentum of ball 2
Resultant momentum = 0.90 kg m/s + 1.00 kg m/s
Resultant momentum = 1.90 kg m/s
Therefore, the magnitude of the resultant momentum before the collision is 1.90 kilogram meters/second.
None of the provided options match the calculated magnitude.