A train moving with constant velocity travels 190 m north in 12 and an undetermined distance to the west. The speed of the train is 36 m/s. Find the direction of the train's motion relative to north.
To find the direction of the train's motion relative to north, we need to determine the angle between the velocity vector of the train and the north direction.
First, let's calculate the time it takes for the train to travel 190 m north. We know that speed (v) is equal to distance (d) divided by time (t), so we can rearrange the formula to solve for time:
t = d / v
Plugging in the values, we have:
t = 190 m / 36 m/s
t ≈ 5.28 s
Now, let's calculate the distance traveled to the west. Since the train is moving with a constant velocity, the distance traveled to the west would be the same as the distance traveled in 12 seconds. Let's call this distance x.
Therefore, the distance traveled to the west (x) is equal to:
x = (36 m/s) * (12 s)
x = 432 m
Now, we have the northward distance (190 m) and the westward distance (432 m). To find the angle between these two directions, we can use trigonometry.
Let's call the angle between the north direction and the train's motion θ. To find θ, we can use the tangent function:
tan(θ) = opposite side / adjacent side
In this case, the opposite side is the northward distance (190 m), and the adjacent side is the westward distance (432 m).
tan(θ) = 190 m / 432 m
Now, to find θ itself, we can take the arctangent (or inverse tangent) of both sides:
θ = arctan(190 m / 432 m)
θ ≈ 23.47°
Therefore, the direction of the train's motion relative to north is approximately 23.47° west of north.