Two objects have the same momentum. which of the following is true? i. the masses of the objects are equal. ii. the speeds of the objects are equal. iii. the velocities of the objects are equal. iv. the direction of motion of each object is the same.

Iv. The direction of motion of each object is the same.

Explanation:

Momentum of an object is defined as:

where

m is the mass of the object

v is its velocity

Since v is a vector, it follows that p is also a vector, and it has the same direction of the velocity. This means that if two objects have same momentum, then the direction of their momentum vector is also the same: therefore, the direction of motion of each object must be the same.

The other options are wrong, because they just state that only one of the two quantities involved in the equation (mass or velocity) is the same, but the two objects can actually have the same momentum even if they have different masses and velocities (in fact, the only thing that matters is that the product between mass and velocity is the same).