4. A plane flies at an airspeed (speed in still air) of 600 miles per hour on a bearing of $\mathrm{N} 50^{\circ} \mathrm{E}$. A west wind (wind from west to east) is blowing at 35 miles per hour. Find the plane's ground speed and direction to the nearest tenth.
Ground speed $=$
Direction (bearing) $=$
Answer
Final Answer: The plane's ground speed is approximately \(\boxed{601.0}\) miles per hour and its direction is approximately \(\boxed{N 53.3^{\circ} E}\).
Step 1 ：Given that the plane's airspeed is 600 miles per hour and the wind speed is 35 miles per hour, we can form a right triangle with these two speeds as the sides. The plane's ground speed will be the hypotenuse of this triangle.
Step 2 ：Using the Pythagorean theorem, we can calculate the ground speed as \(\sqrt{600^2 + 35^2} \approx 601.0\) miles per hour.
Step 3 ：The direction of the plane can be calculated using trigonometric functions. Given the bearing of the plane is \(N 50^{\circ} E\), we can calculate the direction as \(\arctan\left(\frac{35}{600}\right) + 50 \approx 53.3^{\circ}\).
Step 4 ：Final Answer: The plane's ground speed is approximately \(\boxed{601.0}\) miles per hour and its direction is approximately \(\boxed{N 53.3^{\circ} E}\).
