# Projectile Motion of Flying Balloon

1. Apr 7, 2007

### transcendental

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

One dimensional constant acceleration kinematics equations.

3. 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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 7, 2007

### arildno

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

3. Apr 7, 2007

### transcendental

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

4. Apr 7, 2007

### arildno

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:
$$\vec{v}_{p}-\vec{v}_{b}=\vec{v}_{rel}=4.5\vec{i}$$