a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a…
a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a northward current of 5 meters per second, what is the resultant speed of the motorboat rounded to the nearest tenth? 9.4 m/s 8.6 m/s 3.0 m/s 13.0 m/s
Answer
Explanation:
Step1: Identificar los vectores perpendiculares
El movimiento del bote hacia el este es un vector con magnitud $v_1 = 8$ m/s y la corriente del río hacia el norte es un vector con magnitud $v_2=5$ m/s. Son perpendiculares.
Step2: Aplicar el teorema de Pitágoras
La velocidad resultante $v$ se calcula como $v=\sqrt{v_1^{2}+v_2^{2}}$. Sustituyendo $v_1 = 8$ y $v_2 = 5$: $v=\sqrt{8^{2}+5^{2}}=\sqrt{64 + 25}=\sqrt{89}$.
Step3: Calcular el valor numérico
$\sqrt{89}\approx9.4$ m/s.
Answer:
9.4 m/s