Un avión vuela hacia al norte a una velocidad de 90 m/s, pero un fuerte viento sopla hacia al este a 20 m/s y desvía su rumbo. Realiza los trazos y encuentra el vector resultante.
Answers
La adicion de vectores permite encontrar la repuesta para la velocidad resultante del avión es:
Modulo de la veloicdad v= 92,2 m/s Dirección de esta veloicdad 12,5º al Norte del Este
Las magnitudes vectoriales son cantidades tienen modulo y dirección, la velocidad es una de estas magnitudes, por lo tanto deben ser sumada usando álgebra vectorial.
Un sistema de referencia es un sistema desde donde realizar las mediciones, en este caso indican que usemos un sistema de los puntos cardinales.
En el adjunto podemos ver un esquema de los vectores velocidad y su resultante, realicemos el calculo de la resultante por método analíticos
Indican que el valor de la velocidad hacia el Este es vₓ = 20 m/s y la velocidad hacia el Norte es v_y = 90 m/s, por lo tanto, para la magnitud usamos el Teorema de Pitágoras
[tex]R= \sqrt{v_x^2 + v_y^2}[/tex]
R = [tex]\sqrt{20^2 + 90^2}[/tex]
R = 92,2 m/s
Para encontrar la direccion usemos trigonometría
tan θ = [tex]\frac{v_y}{v_x}[/tex]
θ = tan⁻¹ [tex]\frac{v_y}{v_x}[/tex]
θ = tan⁻¹ 20/90
θ = 12,5º
La dirección se lee 12,5º al Norte del Este
En conclusión usando la suma de vectores podemos encontrar la repuesta para la velocidad resultante del avión es:
v= 92,2 m/s con dirección 12,5º al Norte del EsteAprender mas aquí:
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