Question

Un basquetbolista efectúa lo siguientes desplazamientos 6 metros al este 4 metros en dirección noroeste y finalmente 2 metros norte°Cual es la distancia total que recorre?

°Encuentra en forma gráfica el desplazamiento resultante en que dirección actúa y cual es el valor del angulo medido respecto al este​

Answer 1

R = 10.06 m, θ = 28.7º

Step-by-step explanation:

o find the total displacement the best way is to find the displacement in the x (East) and y (North) axes

let's decompose the displacements

d₂ = 4 m

θ₂ = 45

let's use trigonometry

cos 45 = x₂ / d₂

sin 45 = y₂ / d₂

x₂ = d₂ cos 45

y₂ = d₂ sin 45

x₂ = 4 cos 45 = 2,828 m

y₂ = 4 sin 45 = 2,828 m

The shredding the x axis is

x_total = x₁ + x₂

x_total = 6 + 2,828

x_total = 8,828 m

The displacement in the y-axis

y_total = y₂ + y₃

y_total = 2,828 + 2

y_total = 4.828 m

Let's use Pythagoras' theorem for total displacement

R =
`\sqrt{x_(total)^2 + y_(total)^2 }`

R =
`√(8.828^2 + 4.828^2 )`

R = 10.06 m

for the direction let's use trigonometry

tan θ =
`(x_(total) )/(y_(total) )`

θ = tan⁻¹ \frac{x_{total} }{y_{total} }

θ = tan⁻¹
`( 4.828)/( 8.828)`

θ = 28.7º

this angle is measured counterclockwise from the positive side of the x axis (Eat)