# Projectile Motion of Flying Balloon

• transcendental
In summary, the package is thrown horizontally at a velocity of 4.5 m/s relative to the balloon, which is flying upward at a constant velocity of 6.0 m/s. To calculate the time it takes for the package to hit the ground, the vertical motion of the balloon does not need to be included as the package's initial velocity already has a horizontal component. The package's relative velocity to the balloon can be represented as 4.5 m/s in the horizontal direction and -6.0 m/s in the vertical direction. The problem can be solved using one-dimensional constant acceleration kinematics equations.

## Homework Statement

A balloon is flying directly upward with a constant velocity of 6.0 m/s. When it reaches 145 m above the ground, a package is thrown horizontally at 4.5 m/s with respect to the balloon.

How many seconds after being launched will the package hit the ground?

## Homework Equations

One dimensional constant acceleration kinematics equations.

## The Attempt at a Solution

I know how to solve the problem mathematically, but my only issue is whether or not to include the vertical velocity (of the balloon) as the vertical component of the package's motion. If I do this then the package's initial velocity would be at an angle. If I don't include the balloon's motion, then the package would have only a horizontal initial velocity.

Is my thinking correct? Do I include the upward motion of the balloon?

The package's RELATIVE MOTION TO THE BALLOON is said to be horizontal.

So that means when solving the problem, I don't need to include the upward motion, because the horizontal motion of the package is already with respect to the upward moving balloon (the package's initial velocity only has a horizontal component, no vertical). Right?

I think I understand. Thanks

No, no no!

If Vp is package velocity relative to the ground, Vb balloon velocity relative to the ground, and Vrel the package's relative velocity to the balloon, then we have:
$$\vec{v}_{p}-\vec{v}_{b}=\vec{v}_{rel}=4.5\vec{i}$$