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
Please explain how to find this
Thanks
It should have read Physics as subject- I mistyped it-Please help me understand this
To find the resulting velocity of the plane, we need to consider the vectors involved. Let's break down the motion of the plane and the wind into components.
The plane is moving at 120 km/h due west. This can be represented as a vector V_plane = -120 km/h i, where i is the unit vector in the west direction.
The wind is blowing at 40 km/h due east. We can represent this as a vector V_wind = 40 km/h i, where i is the unit vector in the east direction.
To find the resulting velocity, we need to add the vectors V_plane and V_wind. Since they are in opposite directions, we subtract their magnitudes and assign the resulting vector a directional sign according to the larger vector.
Let's calculate the magnitude of the resulting velocity first. Since magnitude is a scalar, it does not take into account the direction. The magnitude of V_plane is 120 km/h, and the magnitude of V_wind is 40 km/h. Therefore, the magnitude of the resulting velocity is |V_resulting| = |V_plane| - |V_wind| = 120 km/h - 40 km/h = 80 km/h.
Now, let's determine the direction of the resulting velocity. Since the plane is moving due west and the wind is blowing due east, the resulting velocity will be more towards the west, but slightly slower than the original velocity of the plane. Therefore, the expression for the plane's resulting velocity can be written as:
V_resulting = -80 km/h i
Comparing this expression to the given options, we see that option (d) 80Vplane matches the resulting velocity expression. So, the correct answer is d. 80Vplane.