Question

A plane is traveling with a velocity of 70 miles/hr with a direction angle of 24 degrees. The wind is blowing at 25 miles/hr with a direction angle of 190 degrees. How fast is the plane moving with the wind blowing on it? Round your answer to the nearest tenth?

Answer 1

46.1 miles/hr

Explanation:

We calculate the x and y coordinates of each vector just like this:

For the plane:

`\begin{gathered} P_x=70\cdot\cos24\degree=63.948\text{ mph} \\ \\ P_y=70\cdot\sin24\degree=28.472\text{ mph} \end{gathered}`

For the wind:

`\begin{gathered} W_x=25\cdot\:\cos190\degree=-24.620\text{ mph} \\ \\ W_y=25\cdot\:\sin190\degree=-4.341\text{ mph} \end{gathered}`

We calculate the resulting vector:

`\begin{gathered} V_x=63.948-24.620=39.328\text{ mph} \\ \\ V_y=28.472-4.341=24.131\text{ mph} \end{gathered}`

Now, we calculate the norm of the vector as follows:

`\begin{gathered} V=√((V_x)^2+(V_y)^2) \\ \\ V=√(\left(39.328\right)^2+\left(24.131\right)^2) \\ \\ V=√(2128.99) \\ \\ V=46.1\text{ mph} \end{gathered}`

The speed of the plane is 46.1 miles per hour.