Question

sumar el siguiente vector y determinar el vector resultante :

3.0 m/s a 45 grados y 5.0 m/s a 135 grados

Answer 1

Sean los vectores a = 3 m/s a 45° ; b = 5 m/s a 135°


Descomponemos a cada uno en sus componentes rectangulares

a = 3 m/s a 45°

ax = a cos(45°) = 3(√2/2) = (3/2)√2

ay = a sen(45°) = 3(√2/2) = (3/2)√2

b = 5 m/s a 135°

bx = b cos(135°) = 5(-√2/2) = (-5/2)√2

by = b sen(135°) = 5(√2/2) = (5/2)√2


Ahora sumamos componente a componente

ax + bx = (3/2)√2 + (-5/2)√2 = -√2

ay + by = (3/2)√2 + (5/2)√2 = 4√2

El vector resultante es a+b = (-√2 , 4√2)