two cars approach a crossroad 36.0m ahead. Car A is traveling east at 9.00m/s and car B is traveling south at 12.0m/s. What is the location of car B relative to car A?
B is NE of A at a distance of 36√2 m
To determine the location of car B relative to car A, we need to find the displacement between the two cars. We can break down the problem into horizontal and vertical components.
First, let's find the time it takes for car A to reach the crossroad. We can use the equation:
time = distance / speed
The distance to the crossroad is given as 36.0 m, and the speed of car A is 9.00 m/s. Therefore, the time taken by car A to reach the crossroad is:
time = 36.0 m / 9.00 m/s = 4.00 s
Now, we can find the horizontal position of car B when car A reaches the crossroad. The horizontal position of car B can be calculated using the equation:
horizontal distance = velocity * time
The velocity of car B in the horizontal direction is 0 m/s, as it is traveling south. Therefore, the horizontal position of car B remains unchanged.
Next, we can find the vertical position of car B when car A reaches the crossroad. The vertical position of car B can be calculated using the equation:
vertical distance = velocity * time
The velocity of car B in the vertical direction is 12.0 m/s, and the time taken for car A to reach the crossroad is 4.00 s. Therefore, the vertical position of car B is:
vertical distance = (12.0 m/s) * (4.00 s) = 48.0 m
So, the location of car B relative to car A is 48.0 m south of car A.