Hot-air balloon (kinematics question)

Sean1218

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

A hot-air balloon is rising upward with a constant velocity of 4.0 m/s. As the balloon reaches a height of 4.0 m above the ground, the balloonist accidentally drops a can of pop over the edge of the basket. How long does it take for the pop can to reach the ground?

2. Relevant equations

d = v2t - 1/2at^2
other uniform acceleration equations

3. The attempt at a solution

Tried a few different things, but nothing seems to work out. I'm not sure if the pop can starts at v1 = 0 m/s or at v1 = 4.0 m/s because of the rising balloon. It falls from 4.0 m and gravity is -9.8 m/s^2.

That's 4 values, but which of the 4 do I use? I didn't get the right answer from just plugging them in, so I'm not sure what else I can do.

fzero

Just to eliminate potential problems, in the velocity term, do you mean v² t, (v2)t, or something else? The equation is either incorrect as written or at least confusing.
This should be an equation for displacement d(t) as a function of:

1. time, t
2. displacement at t=0, d₀
3. velocity at t=0, v₀
4. acceleration, a.

Try to find the appropriate equation. It's close to the one that you wrote.

What was the velocity of the can before it was dropped?

Sean1218

Sorry, meant v2 as in velocity #2.

d = v#2(t) - 1/2at^2 where v#2 = 0, d = 4, a = -9.8, solve for t

if I do it with v#1 instead (v#1 = 4.0), I still don't seem to get the right answer. I must just be plugging in the wrong values, but I've tried everything I can think of.

and the velocity of it before it was dropped was 4.0 m/s, so I guess that'd be v#1, yea.

fzero

I told you to find a more general equation, since you're having trouble identifying how to plug the information given into the equation that you're using. Find the most general equation for displacement at constant acceleration (in your notes or text) and identify the initial and final values that you need to put in.

Sean1218

i thought that was what I did

fzero

It's not, the most general equation is

d(t) = d₀ + v₀ t + (1/2) a t²,

where

d(t) is the displacement after the time t
d₀ is the displacement at t=0
v₀ is the velocity at t=0
a is the constant acceleration.

It's conventional to measure displacement as increasing in the vertical direction. The signs of the initial velocity and acceleration must be identified consistent with that convention.

Try identifying all of the quantities in the equation above in terms of the information given.