A train moving with constant velocity travels 190 north in 14s and an undetermined distance to the west. The speed of the train is 36m/s. Find the direction of the train's motion relative to north. How far west has the train traveled?
To find the direction of the train's motion relative to the north, we need to find the angle that the train's velocity makes with the north direction.
First, let's find the angle that the train's velocity makes with the positive x-axis (east direction). We can use the inverse tangent function:
θ = arctan(vy/vx)
where vy is the northward velocity component and vx is the eastward velocity component of the train's velocity.
In this case, the train only has a northward velocity component vy, since it is not moving in the east direction. Thus, vy = 36 m/s.
Therefore, θ = arctan(36/0) is undefined for our case.
The undefined value of the angle indicates that the train's motion is exactly northward (along the y-axis) with no component in the eastward (x-axis) direction.
To find how far west the train has traveled, we can use the formula for displacement:
distance = velocity * time
In this case, the train traveled northward for 14 seconds with a velocity of 36 m/s. Therefore, the distance it traveled is:
distance = 36 m/s * 14 s = 504 meters
Thus, the train has traveled 504 meters to the west.