Vector problem- Physics?

Question

A plane initially travels 5 km at an angle of 35 degrees to the ground, then climbs at only 10 degrees relative to the ground for 22 km. Determine the magnitude and direction for the vector denoting the total displacement of the plane.

This is what I got:

Total displacement = 25.9 km at an angle of 15 degrees. Is this right?

Answer 1

I have 26.62 km at 14.6 degrees.

Remember the r = √(x^2 + y^2)

Answer 2

This question is not specific enough. Is this 5 km distance travelled by the aeroplane or its component with respect to Earth's surface?

In either case to find a vector sum of two vectors you have to ad their components.

case 1

Let x be a horizontal component and y represent the vertical one.

x = x1 + x2

   =  5km * cos(35deg) + 22km * cos(10deg)

y = 5km * sin(35deg) + 22km * sin(10deg)

total displacement = sq root(x^2 + y^2)

angle = atan (y/x)

case 2

x1 and x2 are given so you need to find ys only.

y1 = 5km * tan(35deg), y2 = 22km * tan(10deg)

Answer 3

sum the x components:

sumX = 5 * Cos(35) + 22 * Cos(10) =25.76 Km

'sum the y components:

sumY = 5 * Sin(35) + 22 * Sin(10) = 6.69 Km

Angle with the positive x-axis: 14.55 degrees

Resultant vector magnitude = sqr(25.76^2+6.69^2) =26.62 Km