An airplane flies toward 124° at 525 km/h. What is the component of the plane's velocity
(a) toward 90°?
km/h
(b) toward 180°?
km/h
To find the component of the plane's velocity in a given direction, we can use trigonometry.
In this case, we have the plane flying at an angle of 124° with a speed of 525 km/h. We want to find the component of velocity toward 90° and toward 180°.
(a) To find the component of velocity toward 90°, we need to find the perpendicular component of the velocity. Since the plane is flying at an angle of 124°, the perpendicular component will be the sine of this angle multiplied by the velocity.
The formula to find the perpendicular component of the velocity is:
perpendicular component = velocity * sin(angle)
In this case, the angle is 124° and the velocity is 525 km/h:
perpendicular component = 525 km/h * sin(124°)
Using a calculator, we can find that sin(124°) is approximately 0.821 and calculate the perpendicular component:
perpendicular component = 525 km/h * 0.821 ≈ 430 km/h
So, the component of the plane's velocity toward 90° is approximately 430 km/h.
(b) To find the component of velocity toward 180°, we need to find the horizontal component of the velocity. Since the plane is flying at an angle of 124°, the horizontal component will be the cosine of this angle multiplied by the velocity.
The formula to find the horizontal component of the velocity is:
horizontal component = velocity * cos(angle)
In this case, the angle is 124° and the velocity is 525 km/h:
horizontal component = 525 km/h * cos(124°)
Using a calculator, we can find that cos(124°) is approximately -0.571 and calculate the horizontal component:
horizontal component = 525 km/h * (-0.571) ≈ -299 km/h
Note that the negative sign indicates the direction is opposite to the positive x-axis.
So, the component of the plane's velocity toward 180° is approximately -299 km/h.