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

Question

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 1.2 s. Find the time it takes for the ball to fall from rest all the way to the ground.

I WILL GIVE TONS OF POINTS AWAY TO WHOEVER ANSWERS THIS CORRECTLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 

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Calantha 4 years 2021-08-10T17:00:44+00:00 1 Answers 402 views 0

Answers ( )

  1. minhkhoi
    0
    2021-08-10T17:02:07+00:00
    Reply

    Answer:

    1.697s

    Explanation:

    We use the second equation of free fall under gravity as follows;

    h=ut+\frac{1}{2}gt^2...............(1)

    Since  the ball fell freely, u = 0m/s, therefore equation (1) reduces to

    h=\frac{1}{2}gt^2...............(2)

    Given that h is the total height the ball falls through in time t seconds.

    However, according to the stated problem the ball falls halfway in 1.2s, this simply implies that the ball falls through a distance of \frac{h}{2} in 1.2s. Hence we can write the following, given that g=9.8m/s^2;

    \frac{h}{2}=\frac{1}{2}*9.8*1.2^2\\hence\\h=9.8*1.2^2\\h=14.112m

    We can now proceed to find the time t for which it falls through h = 14.112m as follows;

    14.112=\frac{1}{2}*9.8*t^2\\14.112=4.9t^2\\t^2=\frac{14.112}{4.9}\\t^2=2.88\\t=\sqrt{2.88} \\t=1.697s

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