A plane flies due north at 300km/h but a crosswind blows north-west at 40km/h. Find the resultant velocity of the plane.
Once I have drawn I diagram it is often okay, but it is the initial steps that I struggle with.
So make sketch ,
on the y-axis mark off 300
From there draw a 45° angle line ( NW) and make it 40 units
Joint the endpoint to the origin.
That last line is your resultant
I see a cosine law application
Two sides of 300 and 40 with an angle of 135° between them
To find the resultant velocity of the plane, we can break down the velocities into their north and west components.
First, let's consider the plane's velocity. The plane is flying due north at a speed of 300 km/h. Since the plane is flying directly north, there is no westward component to its velocity.
Next, let's consider the crosswind's velocity. The crosswind blows northwest at a speed of 40 km/h. To determine the westward component of the crosswind's velocity, we need to find the horizontal component of the crosswind's velocity.
Since the crosswind blows northwest, it makes a 45-degree angle with the west direction (northwest is halfway between north and west). This means that the westward component of the crosswind's velocity is the same as the northward component because the two components have the same magnitude.
Now, let's find the magnitude of the westward component of the crosswind's velocity using trigonometry. We can use the formula: sin(45) = opposite/hypotenuse.
sin(45) = westward component / 40 km/h
Solving for the westward component:
westward component = sin(45) * 40 km/h
westward component = 28.284 km/h
Since the westward component of the crosswind's velocity is in the opposite direction of the plane's northward velocity, we subtract the westward component from the plane's northward velocity to find the resultant velocity:
resultant velocity = 300 km/h - 28.284 km/h
resultant velocity = 271.716 km/h
Therefore, the resultant velocity of the plane is approximately 271.716 km/h in the north direction.