Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of 24 kg . m/s, and Fido runs northward with momentum 10 kg . m/s. They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision?
A) 14 kg . m/s
B) 26 kg . m/s
C) 34 kg . m/s
D) It cannot be determined without knowing the masses and velocities of the dogs.
M1V1 + M2V2 = 24 + 10i
sqrt(24^2+10^2) = 26kg.m/s = Total momentum before collision = Total momentum AFTER collision.
To find the magnitude of their combined momentum after the collision, we need to add their individual momenta together. However, we cannot determine the answer without knowing the masses and velocities of the dogs since momentum depends on both mass and velocity. Therefore, the answer is D) It cannot be determined without knowing the masses and velocities of the dogs.
To find the magnitude of their combined momentum after the collision, we need to use the law of conservation of momentum. According to this law, the total momentum before the collision must be equal to the total momentum after the collision.
Given that Rover has a momentum of 24 kg . m/s to the east and Fido has a momentum of 10 kg . m/s to the north, we need to find the combination of these momenta.
To do this, we can treat momenta as vectors in a coordinate system. Rover's momentum can be represented as a vector pointing to the right (eastward), and Fido's momentum can be represented as a vector pointing upwards (northward). Adding these vectors will give us the resultant vector, which represents the combined momentum after the collision.
To add the vectors, we can use the Pythagorean theorem. The magnitude of the combined momentum is given by:
(combined momentum)^2 = (Rover's momentum)^2 + (Fido's momentum)^2
Plugging in the numbers, we have:
(combined momentum)^2 = (24 kg . m/s)^2 + (10 kg . m/s)^2
Simplifying:
(combined momentum)^2 = 576 kg^2 . m^2/s^2 + 100 kg^2 . m^2/s^2
(combined momentum)^2 = 676 kg^2 . m^2/s^2
Taking the square root of both sides:
combined momentum = √(676 kg^2 . m^2/s^2) = 26 kg . m/s
Therefore, the correct answer is B) 26 kg . m/s.