an airplane flies at 150 mph and heads N 30 degrees east. A 40 mph wind blows it in the direction S 30 degrees E. What is the planes resultant velocity
convert to rectangular form
add up the x- and y-components
convert back to magnitude and direction
To find the plane's resultant velocity, we can use vector addition.
First, let's break down the given velocities into their northward (N) and eastward (E) components.
The airplane's velocity of 150 mph at an angle of N 30 degrees E can be split into a northward component and an eastward component.
The northward component is given by:
150 mph * cos(30) = 150 * √3/2 ≈ 129.9 mph (rounded to the nearest tenth)
The eastward component is given by:
150 mph * sin(30) = 150 * 1/2 = 75 mph
Now, let's do the same for the wind's velocity of 40 mph in the direction S 30 degrees E.
The southward component is given by:
40 mph * cos(30) = 40 * √3/2 ≈ 34.6 mph (rounded to the nearest tenth)
The eastward component is given by:
40 mph * sin(30) = 40 * 1/2 = 20 mph
To find the resultant velocity, we need to add the components together separately for the northward and eastward directions.
For the northward direction:
The northward component of the airplane's velocity (129.9 mph) minus the southward component of the wind's velocity (34.6 mph) gives us:
129.9 mph - 34.6 mph = 95.3 mph (rounded to the nearest tenth)
For the eastward direction:
The eastward component of the airplane's velocity (75 mph) plus the eastward component of the wind's velocity (20 mph) gives us:
75 mph + 20 mph = 95 mph
Therefore, the plane's resultant velocity is approximately 95.3 mph towards N 95 degrees E.