Help with kinematics in one dimension free fall

[xlaserx7]

Homework Statement

A wrecking ball is hanging at rest from a crane when suddenly the cable breaks. The time it taktes 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

Homework Equations

v=vo + at

The Attempt at a Solution

0 = 4.6 + (-9.80)t
t = - 5.2 s. time can't be negative so 5.2s

 

[rl.bhat]

Use the equation h = vo*t + 1/2*g*t^2
Using vo = 0 and t = 1.2s find the half height and then full height. From that find the time to fall from rest to the ground.

 

[xlaserx7]

i don't understand why can't i use v=vo + at
and did i mess up on the time?

 

[xlaserx7]

0 times 1.2 + .5 (-9.80)(1.44) = -7.056 gives me the height. full height is 7.056 times 2 = 14.112
now i am stuck again >.<

wait... now i use v=vo + at to find the final so

0 + (-9.80)1.2 = 11.76 = final velocity

then i use y = 1/2 ( v + v )t

y = 1/2(0 + -11.76)1.2
y = -7.056 omg i got the same thing?

 

[LowlyPion]

Maybe look at it this way:

The distance dropped from rest is equal to 1/2 a*t².

Exploiting this observe then that

$$\frac{H_1}{H_2} =\frac{1/2*g*t_1^2}{1/2*g*t_2^2}$$

This simplifies to - plugging in that H1 = H , and H2 = 2H

$$\frac{H}{2H} = \frac{1.2^2}{t_2^2} = \frac{1}{2}$$

$$t_2 = 1.2 * \sqrt{2}$$

Evaluating this equation looks remarkably easier to me.

 

[xlaserx7]

ahh thank you

 

[LowlyPion]

ahh thank you

So long as you learn the technique, you're welcome.

Good luck.