if an airplane is flying directly north at 300.0 km/h, and a crosswind is hitting the airplane at 50.0 km/h…

if an airplane is flying directly north at 300.0 km/h, and a crosswind is hitting the airplane at 50.0 km/h from the east, what is the airplanes resultant velocity? (use the graphical method to answer and include your scale on the graph paper.) give both the magnitude and the angle in your answer.

if an airplane is flying directly north at 300.0 km/h, and a crosswind is hitting the airplane at 50.0 km/h from the east, what is the airplanes resultant velocity? (use the graphical method to answer and include your scale on the graph paper.) give both the magnitude and the angle in your answer.

Answer

Explanation:

Step1: Identificar vectores

El avión vuela hacia el norte a $v_y = 300.0$ km/h y el viento viene del este a $v_x=50.0$ km/h.

Step2: Calcular magnitud del vector resultante

Usando el teorema de Pitágoras, $v=\sqrt{v_x^{2}+v_y^{2}}=\sqrt{(50.0)^{2}+(300.0)^{2}}=\sqrt{2500 + 90000}=\sqrt{92500}\approx304.1$ km/h.

Step3: Calcular el ángulo

Usando la tangente, $\theta=\arctan\left(\frac{v_x}{v_y}\right)=\arctan\left(\frac{50.0}{300.0}\right)=\arctan\left(\frac{1}{6}\right)\approx9.46^{\circ}$ al este del norte.

Answer:

Magnitud: $304.1$ km/h, Ángulo: $9.46^{\circ}$ al este del norte.