Given vectors d (3.00 m, 315 degrees wrt x-axis) and e (4.50 m, 53.0 degrees wrt x-axis), find the resultant r= d + e. (a) write r in vector form. (b) write r showing the magnitude and direction in degrees.

Explanation:

Knowing the magnitude and directions relative to the x axis, we can find the Cartesian representation of the vectors using the formula

where its the magnitude and θ.

So, for our vectors, we will have:

and

Now, we can take the sum of the vectors

This is R in Cartesian representation, now, to find the magnitude we can use the Pythagorean theorem

To find the direction, we can use

As we are in the first quadrant, this is relative to the x axis.

d. air pressure decreases as altitude increases.