a plane is flying due east in still air at 395km/h suddenly the plane is hit by wind blowing at 55km/h toward the west. what is the resultant of the plane?
If the positive direction is east, we have to add up the two velocities:
395 - 55 = 340
or, 340km/h east
To find the resultant of the plane, we need to consider the velocity vectors of the plane and the wind.
Given:
Velocity of the plane in still air (Vp) = 395 km/h towards the east
Velocity of the wind (Vw) = 55 km/h towards the west
To find the resultant, we need to subtract the velocity of the wind from the velocity of the plane.
Resultant velocity (Vr) = Vp - Vw
Taking into consideration the directions:
Vp (eastward) - Vw (westward) = Vp + (-Vw)
Vp = 395 km/h (eastward)
-Vw = -(-55) km/h = 55 km/h (eastward)
Vr = Vp + (-Vw)
= 395 km/h + 55 km/h
= 450 km/h towards the east
Therefore, the resultant velocity of the plane is 450 km/h towards the east.
To find the resultant of the plane, we need to determine the combined effect of the plane's velocity (due east) and the wind's velocity (toward the west). The resultant will give us the direction and magnitude (speed) of the plane's movement relative to the ground.
To find the resultant, we need to use vector addition. A vector is a quantity that has both magnitude and direction. In this case, the plane's velocity and the wind's velocity are vectors.
Given that the plane's velocity is due east at 395 km/h and the wind's velocity is blowing toward the west at 55 km/h, we can consider the plane's velocity as positive and the wind's velocity as negative.
Vector addition involves adding the magnitudes of the vectors and considering their directions. When adding vectors in opposite directions, we subtract their magnitudes.
In this case, to find the resultant, we need to subtract the magnitude of the wind's velocity from the magnitude of the plane's velocity, while keeping the same direction as the plane's velocity.
Therefore, the resultant velocity of the plane is 395 km/h - 55 km/h = 340 km/h, still in the eastward direction.