How can I solve this free fall problem with missing variables?

[pinky2468]

Stumped on free fall problem!

This is probably an easy question, but I am stumped!A wrecking ball is hanging at rest from a crane when suddenly the cable breaks. The time it takes for the ball to fall halfway to the ground is 1.2s. Find the time it takes for the ball to fall from rest all the way to the ground

 

[Doc Al]

What kind of motion does the ball undergo? Show us what you've done so far.

 

[pinky2468]

I know that the acceleration due to gravity is -9.81m/s2. The part that really confuses me is the fact that the time given is only part of the way down. Should I find the displacement or the velocity to solve the problem? I don't want the answer, just the direction to go in.
Thanks!

 

[Doc Al]

Since you have information about distance and time, you'll need an equation showing how distance depends on time for accelerated motion. What's that equation?

 

[Beer-monster]

I would go with displacement, as the velocity increases. You have enough to find the distance dropped in 1.2s, which the question states is half way. Double that and you have the full distance then you should be able to find the time taken do drop all the way.

 

[pinky2468]

I don't have information on the distance, all I have is 1/2 the time and acceleration.
I know the major equations that I could use but I don't understand how to use them if I don"t have enough information to enter in them.

 

[Doc Al]

You have all the information you need about the distance. Call the total distance to the ground D. Set up two equations: one for half the distance (D/2) and time T_1 = 1.2; the other for the full distance D and T_2. Do it and see if you can solve for T_2. (Hint: don't be in a hurry to plug in numbers--things will cancel.)

 

[pinky2468]

Thank you beer monster! I got the right answer, I can't believe how easy the solution was!

 

[Beer-monster]

Don't forget to thank Doc Al, he was basically telling you the same thing. Actually he was doing a better job than me as he was trying to get you to think out the solution.

Something about the equations of kinematics, is they all have a missing variable. So there is usually a way to work out something from any piece of info, and from that something you can use another equation to get your answer.