At an antique car rally, a Stanley Steamer automobile travels north at 38 km/h and a Pierce Arrow automobile travels east at 51 km/h. Relative to an observer riding in the Stanley Steamer, what are the x- and y-components of the velocity of the Pierce Arrow car?
To determine the x- and y-components of the velocity of the Pierce Arrow car relative to the observer in the Stanley Steamer, we can use vector addition.
Let's consider the x-axis to represent the east-west direction and the y-axis to represent the north-south direction. The Stanley Steamer is moving north at 38 km/h, so its velocity can be represented as (0, 38) km/h. The Pierce Arrow, on the other hand, is moving east at 51 km/h, so its velocity can be represented as (51, 0) km/h.
To find the relative velocity of the Pierce Arrow with respect to the Stanley Steamer, we need to add the two velocities together. So, we add the corresponding components:
x-component: 0 + 51 = 51 km/h
y-component: 38 + 0 = 38 km/h
Therefore, the x-component of the velocity of the Pierce Arrow car relative to the observer in the Stanley Steamer is 51 km/h, and the y-component is 38 km/h.