An airplane flying at 120km/h due west moves into a region where the wind is blowing at 40km/h due east. If the plane's original vecotr velocity is Vplane, what is the expression for the plane's resulting velocity in terms of Vplane.
a. 1/3 >Vplane
b. 2/3>Vplane
c.1 Vplane
d. 80Vplane
What is 80/120?
To find the resulting velocity of the plane, we need to subtract the velocity due to the wind from the velocity of the plane.
The velocity of the plane (Vplane) is given as 120 km/h due west. Since it is moving due west, the velocity is negative.
The velocity of the wind is given as 40 km/h due east. Since it is moving due east, the velocity is positive.
To subtract these velocities, we can write it as:
Resulting velocity = Vplane - Velocity of the wind
Since the velocity of the wind is positive, we need to subtract a positive value from a negative value. This means that the magnitude of the resulting velocity will be smaller than the magnitude of the plane's velocity.
Therefore, the expression for the plane's resulting velocity in terms of Vplane is:
Resulting velocity = Vplane - 40 km/h
None of the given answer choices match this expression exactly. However, since the magnitude of the resulting velocity is smaller than the magnitude of the plane's velocity, we can eliminate answer choices c and d, as they would give a resulting velocity equal to or greater than the plane's velocity.
Answer choices a and b both suggest that the resulting velocity is a fraction of Vplane. Since the wind speed is relatively small compared to the plane's speed, it is reasonable to assume that the resulting velocity would be only slightly smaller than the plane's velocity.
Therefore, the closest answer choice is:
b. 2/3 > Vplane