An airplane is flying with a speed of 240 km/hr at an angle of 27 degrees north of east.
a) How fast is the plane flying north?
b) How fast is the plane flying east?
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To solve this problem, we can break down the airplane's velocity into its northward and eastward components.
a) To find how fast the plane is flying north, we need to find the northward component of the velocity. This can be done using trigonometry. We use the angle north of east to determine how much of the total 240 km/hr velocity is in the northward direction.
First, we need to find the value of the north component using the given angle:
North component = Total velocity * sin(angle)
= 240 km/hr * sin(27 degrees)
To calculate this, we need to convert the angle from degrees to radians, as trigonometric functions in most programming languages work with radians. To do this, we can use the formula:
angle in radians = angle in degrees * pi / 180
Using this formula, we can find the north component:
North component = 240 km/hr * sin(27 degrees * pi / 180)
Calculating this expression will give us the speed at which the plane is flying north.
b) To find how fast the plane is flying east, we need to find the eastward component of the velocity. We use the angle north of east to determine how much of the total 240 km/hr velocity is in the eastward direction.
To calculate the east component, we use the formula:
East component = Total velocity * cos(angle)
= 240 km/hr * cos(27 degrees)
Applying the same conversion from degrees to radians, we can calculate the east component of the velocity.
Calculating these expressions will give us the speed at which the plane is flying north and east respectively.
Resolve into the two directions.
For north, use Vsin(θ) and for east, use Vcos(θ).