I have a question
An airplane is flying at 120km/h due west moves into a region where the wind is blowing at 40km/h. If the planes original velocity is Vplane, what is the expression for the plane's resulting velocity in terms of V plane?
Answers are given 1/3 greater than Vplane
2/3 greater than Vplane
1 v Plane
80Vplane
I think it is 80vplane because you have to subtract the two velocitiesbit a friend of mine doing the same problem said it was 2/3 greater than vplane-I don't think is correct
To calculate the resulting velocity of the plane, you need to consider the effect of the wind on the plane's motion. Here's how you can approach the problem:
1. Given that the plane's original velocity is Vplane = 120 km/h due west, and the wind is blowing at 40 km/h (let's call this velocity Vwind).
2. Remember that velocities are vectors and have both magnitude (speed) and direction. In this case, the plane's velocity is due west, and the wind's velocity is also due west.
3. Since the wind is blowing in the same direction as the plane's motion, it will add to the plane's velocity. To find the resulting velocity, you can simply add the two velocities together.
4. The resulting velocity (Vresultant) can be found using the equation: Vresultant = Vplane + Vwind.
5. Since both Vplane and Vwind are in the same direction (due west), their magnitudes can be added: Vresultant = 120 km/h + 40 km/h.
6. Simplify the expression: Vresultant = 160 km/h.
Hence, the expression for the plane's resulting velocity in terms of Vplane is 160 km/h (not any of the options provided). Therefore, the correct answer is not among the given options.
To find the expression for the plane's resulting velocity, we need to consider the effect of the wind on the plane's motion.
Since the wind is blowing towards the east and the plane is flying towards the west, we can subtract the magnitude of the wind speed from the plane's speed. This will give us the overall speed and direction of the plane with respect to the ground.
Let V_plane be the plane's original velocity. Since it is flying due west, its velocity can be represented as -V_plane (negative sign indicates the direction).
The wind is blowing towards the east at a speed of 40 km/h. Thus, the wind's velocity can be represented as +40 km/h (positive sign indicates the direction).
The resulting velocity of the plane can be calculated using the vector sum of the two velocities:
Resulting velocity = Plane's velocity + Wind's velocity
Resulting velocity = -V_plane + 40
Simplifying this expression, we get:
Resulting velocity = 40 - V_plane
Therefore, the expression for the plane's resulting velocity in terms of V_plane is 40 - V_plane.
None of the given answers match this expression exactly. However, if we substitute V_plane = 80 km/h into the expression 40 - V_plane, we get:
Resulting velocity = 40 - (80) = -40 km/h
So it seems like there might be an error in the given answer choices, or an oversight in our calculations.