The x component of vector upper a overscript right-arrow endscripts is -22.5 m and the y component is +54.1 m. (a) what is the magnitude of upper a overscript right-arrow endscripts? (b) what is the angle between the direction of upper a overscript right-arrow endscripts and the positive direction of x?

Magnitude = √(x-component)² + (y-component)²

Magnitude = √(-22.5m)² + (54.1m)²

Magnitude = √(506.25m² + 2926.81m²)

Magnitude = √(3,433.06 m²)

Magnitude = 58.6 meters

Direction = arctan(y-component/x-=component)

Direction = arctan(-54.1m/22.5m)

Direction = arctan(-2.404)

The angle between the direction of upper a overscript right-arrow endscripts and the positive direction of x is 67.4°.  

That is, the vector upper a overscript right-arrow endscripts is in the 4th quadrant, a little below southeast, pointing from the origin in the direction of  67.4 degrees below the positive x-axis.

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s

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