a novice pilot sets a plane's controls, thinking the plane will fly at 2.5X10^2 km/h to the north. if the wind blows at 75 km/h toward the southeast, what is the planes's resultant velocity?
204 km/h at 75 degrees north of east
change the SE vector to S + E, Add to the N vector.
99.48 km/h
To find the plane's resultant velocity, we need to consider the vector sum of its velocity and the velocity of the wind.
First, we'll break down the given velocities into their respective components:
1. The plane's velocity: 2.5 x 10^2 km/h to the north.
- North component: 0 km/h (since the plane is directly moving north)
- East component: 2.5 x 10^2 km/h (there is no eastward movement)
2. The wind's velocity: 75 km/h toward the southeast.
- Southeast component: 75 km/h (since the wind is directly moving southeast)
To determine the resultant velocity, we need to add the respective components together. However, since the plane's velocity only has a north component and no east component, we only need to calculate the north component of the resultant velocity.
To get the north component of the resultant velocity, we subtract the southeast component of the wind's velocity from the north component of the plane's velocity:
Resultant north component = Plane's north component - Wind's southeast component
Resultant north component = 0 km/h - 75 km/h
Resultant north component = -75 km/h
The negative sign indicates that the resultant velocity is in the opposite direction of what was initially assumed. Thus, the plane's resultant velocity is 75 km/h to the south.