Question

The mathematical definition of momentum is that it is the quantity given by the product of the mass and velocity of an object. Since velocity is a vector quantity, so then is momentum. Recall that vector quantities are described by both magnitude and direction, whereas scalar quantities, e.g., speed, do not consider direction, only magnitude. We have used vectors for velocity and force situations, now momentum because of its relationship to velocity. Consider a 100 kg hockey player skating at 10 m/s in the northeast direction on a rink where the east-west directions establish the x-axis (east being positive) of a coordinate system. Similarly, the north-south directions establish the y-direction (north being positive). What are the x and y components of this skater's momentum?

	Px = 500 Ns, Py = 866 Ns
	Px = 866 Ns, Py = 500 Ns
	Px = 500 Ns, Py = 500 Ns
	Px = 1000 Ns, Py = 1000 Ns
	Px = 707 Ns, Py = 707 Ns
	None of these are correct.

Answer 1

Momentum is given by:

P = m*V

m = mass of player = 100 kg

V = Velocity of player = 10 m/sec in north-east direction = 10 m/sec at 45 deg North of east

Using component method

Vx i + Vy j = V*cos i + V*sin j

Vx = x-component of velocity = 10*cos 45 deg = 7.07 m/sec

Vy = y-component of velocity = 10*sin 45 deg = 7.07 m/sec

So,

P = m*(Vx i + Vy j)

P = 100*(7.07 i + 7.07 j)

P = 707 i + 707 j

Px = 707 N.sec and Py = 707 N.sec

Correct option is E.