Combining Velocities

Sometimes the motion of an object involves more than one velocity.

Two or more velocities add by vector addition. The velocity of the river relative to the riverbank (X) and the velocity of the boat relative to the river (Y) in Figure 10A combine. They yield the velocity of the boat relative to the riverbank (Z). This velocity is 17 kilometers per hour downstream.

In Figure 10B, the relative velocities of the current (X) and the boat (Y) are at right angles to each other. Adding these velocity vectors yields a resultant velocity of the boat relative to the riverbank of 13 km/h (Z). Note that this velocity is at an angle to the riverbank.

Figure 10 Vector addition is used when motion involves more than one velocity. A The velocity of the boat in the reference frame of the riverbank (17 km/h) is a combination of the relative velocities of the boat and the river. B You can determine the resultant velocity of the boat relative to the riverbank (13 km/h) by measuring from the tail of one vector to the head of the other.