Question

A 4.00 kg ball is moving at 4.00 m/s to the EAST and a 6.00 kg ball is moving at 3.00 m/s to the NORTH. The total momentum of the system is:___________.A. 14.2 kg m/s at an angle of 48.4 degrees SOUTH of EAST.B. 48.2 kg m/s at an angle of 24.2 degrees SOUTH of EAST.C. 48.2 kg m/s at an angle of 48.4 degrees NORTH of EAST.D. 24.1 kg m/s at an angle of 24.2 degrees SOUTH of EAST.
E. 24.1 kg m/s at an angles of 48.4 degrees NORTH of EAST.

Answer 1

Answer:

The total momentum is 24.1 kg m/s at an angle of 48.4 degrees NORTH of EAST

Explanation:

Momentum = mass*velocity of a body

For a 4.00 kg ball is moving at 4.00 m/s to the EAST, its momentum = 4*4 = 16kgm/s

For a 6.00 kg ball is moving at 3.00 m/s to the NORTH;

its momentum = 6*3 = 18kgm/s

Total momentum = The resultant of both momentum

Total momentum = √16²+18²

Total momentum = √580

total momentum = 24.1kgm/s

For the direction:

$\theta = tan^{-1} \frac{y}{x}\\\theta = tan^{-1} \frac{18}{16}\\ \theta = tan^{-1} 1.125\\\theta = 48.4^{0}$

The total momentum is 24.1 kg m/s at an angle of 48.4 degrees NORTH of EAST