Question

In reaching her destination, a backpacker walks with an average velocity of 1.20 m/s, due west. This average velocity results, because she hikes for 5.63 km with an average velocity of 2.33 m/s due west, turns around, and hikes with an average velocity of 0.374 m/s due east. How far east did she walk (in kilometers)?

Answer 1

Answer:

$x_2 = 648.46\ m$

Explanation:

given,

Average velocity due west =  1.20 m/s

case 1

Distance moved in west, x₁ = 5.63 km

speed due west, v₁ = 2.33 m/s

Case 2

Distance moved in east = x₂

speed due east, v₂ = 0.374 m/s

total distance = x₁ + x₂ = 5.62

total time = t₁ + t₂ = 5630/2.33 + x₂/0.374

now,

$average\ velocity = \dfrac{total\ distance}{total\ time}$

$-1.20= \dfrac{-5630 + x_2}{\dfrac{5630}{2.33}+\dfrac{x_2}{0.374}}$

negative sign is used because we want the distance in east but velocity is in west.

$- 2900 - 3.21 x_2 = -5630 + x_2$

$-4.21 x_2 = -2730$

$x_2 = 648.46\ m$

The distance she walked in east is equal to 648.46 m