Question

A plane traveling north at 100.0 km/h through the air gets caught in a 40.0 km/h crosswind blowing west. This turbulence caused a beverage cart to brake free and begin rolling at 20.0 km/h toward the tail of the plane. What is the velocity of the cart relative to the ground? (you do not have to convert these since they are all the same unit)

Answer 1

Answer:

The velocity $\vec{v}_{c/g}$ of the cart with respect to the ground is

$\vec{v}_{c/g}=-40\hat{x}+80\hat{y}\, km/h$

if we consider North the positive y-direction and East the positive x-direction.

Explanation:

We have for relative motion the following expression:

$\vec{v}_{c/g}=\vec{v}_{c/p}+\vec{v}_{p/g}$

Where $\vec{v}_{c/g}$ is the velocity of the cart with respect to the ground, $\vec{v}_{c/p}$ is the velocity of the cart with respect to the plane and $\vec{v}_{p/g}$ is the velocity of the plane with respect to the ground.

We find that:

$\vec{v}_{c/p}=-20\hat{y}$

$\vec{v}_{p/g}=-40\hat{x}+100\hat{y}$

Thus:

$\vec{v}_{c/g}=-20\hat{y}-40\hat{x}+100\hat{y}=-40\hat{x}+80\hat{y} \, km/h$