Kinetics Problem: Finding time distance and initial velocity

[kevinxt]

Homework Statement

You are riding in a hot air balloon at an altitude of 167 meters traveling at a horizontal speed of 24 m/s. If you fall out of the basket, how long will it take you to hit the ground? How far will you travel horizontally in this time. What is your total speed when you hit the ground?

Homework Equations

Vyf=Vyo-ag*t
y=Vyo*t-1/2ag*t^2

The Attempt at a Solution

My horrendous knowledge of physics has led to this. I used the second equation and I got: 167=Vyo*t-4.9t^2.
So basically I don't know the initial velocity or time in the equation and I'm sooooo confused. :(
I appreciate all the help.

 

[SteamKing]

Homework Statement

You are riding in a hot air balloon at an altitude of 167 meters traveling at a horizontal speed of 24 m/s. If you fall out of the basket, how long will it take you to hit the ground? How far will you travel horizontally in this time. What is your total speed when you hit the ground?

Homework Equations

Vyf=Vyo-ag*t
y=Vyo*t-1/2ag*t^2

The Attempt at a Solution

My horrendous knowledge of physics has led to this. I used the second equation and I got: 167=Vyo*t-4.9t^2.
So basically I don't know the initial velocity or time in the equation and I'm sooooo confused. :(
I appreciate all the help.

The equation you selected is correct. Re-read the problem statement carefully: "You are riding in a hot air balloon at an altitude of 167 meters traveling at a horizontal speed of 24 m/s."

Is the balloon changing its altitude, up or down, according to this description? If it isn't changing altitude, what additional information can you plug into your equation? After adding this information, can you solve for the amount of time it takes to fall before you hit the ground?

 

[kevinxt]

The equation you selected is correct. Re-read the problem statement carefully: "You are riding in a hot air balloon at an altitude of 167 meters traveling at a horizontal speed of 24 m/s."

Is the balloon changing its altitude, up or down, according to this description? If it isn't changing altitude, what additional information can you plug into your equation? After adding this information, can you solve for the amount of time it takes to fall before you hit the ground?

I feel silly for not understanding the problem. So, the balloon is not changing altitude. If it isn't changing altitude, my initial vertical velocity is 0 since gravity is the only force affecting the rate of the falling object?

And also, to find distance traveled horizontally I would use the time found above and multiply that by 24 m/s.
To find velocity I would use the equation v=d/t and take 167/time, which I had found above?

 

[SteamKing]

I feel silly for not understanding the problem. So, the balloon is not changing altitude. If it isn't changing altitude, my initial vertical velocity is 0 since gravity is the only force affecting the rate of the falling object?

This is correct.

And also, to find distance traveled horizontally I would use the time found above and multiply that by 24 m/s.

This is also correct.

To find velocity I would use the equation v=d/t and take 167/time, which I had found above?

This will only give you an 'average' velocity.

Think carefully here. When you fall from the balloon, your velocity in the vertical direction is changing due to the acceleration by gravity. Your body also has a horizontal velocity due to the travel of the balloon. How to reconcile these two different velocities? Hint: Think vectors.

Also, what does the first equation from the OP tell you about the vertical velocity?

 

[kevinxt]

So I use the first equation in the OP: Vyf=Vyo-ag*t to find Vyf. Then I would need to find Vxf with the equation Vxf=Vxo+a*t. I could then use v^2=vyf^2+vxf^2.

 

[SteamKing]

So I use the first equation in the OP: Vyf=Vyo-ag*t to find Vyf. Then I would need to find Vxf with the equation Vxf=Vxo+a*t. I could then use v^2=vyf^2+vxf^2.

This is correct.

 

[kevinxt]

Thank you sooooo much! I greatly appreciate your help. :)