Calculating Height & Time of a Falling Ball | Physics Problem Solution

[Manni]

A ball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall. a) From what height was the ball dropped? b) What was the total time of the fall?

Hey, I don't know how to approach these types of problems. Help?

 

[Delphi51]

Hi Manni. The approach is nearly always to ask, "What type of motion is it? What formulas apply?" Once you can write a formula for the height as a function of time, you'll be able to apply a bit of math to it and find the answers!

 

[Manni]

It's 1 dimensional motion in the y-direction. As for the equations, there's 2 that I can think of off the top of my head:

Velocity = v(initial) + at
Position = x(initial) + (0.5)[ v(initial) + v ]t

I don't know what to do from there.

 

[Delphi51]

Position = x(initial) + (0.5)[ v(initial) + v ]t

should be y = yi + Vi*t + ½ a⋅t²

How do we put in

A ball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall.

Have to do something with "last second" for starters!
Maybe find the time to fall from height Yi. Then subtract 1 to get the time at the point where it still has 3/4 of the distance to fall.

To find the time to fall, work with the second equation and solve for t.