An open paint bucket of mass 12kg is attached to another paintbucket of mass 9kg

Question

An open paint bucket of mass 12kg is attached to another paintbucket of mass 9kg by a light rope 21m long. The light bucket is atrest on the ground, and the rope goes up and over a smallfrictionless pulley and is attached to the heavy bucket. Theheavybucket is on a window sill 11m above the top of the bucket onthe ground. There is no slack in the rope. If the heavy bucketslips off the window sill, how long will it be until the bucketscollide and the first big splash occurs? This problem looks very easy and I did the problem, but I'mgetting a different answer. I keep checking but I don't know whereI'm doing wrong. The answer is supposed to be 2.8 seconds. An open paint bucket of mass 12kg is attached to another paintbucket of mass 9kg by a light rope 21m long. The light bucket is atrest on the ground, and the rope goes up and over a smallfrictionless pulley and is attached to the heavy bucket. Theheavybucket is on a window sill 11m above the top of the bucket onthe ground. There is no slack in the rope. If the heavy bucketslips off the window sill, how long will it be until the bucketscollide and the first big splash occurs? This problem looks very easy and I did the problem, but I'mgetting a different answer. I keep checking but I don't know whereI'm doing wrong. The answer is supposed to be 2.8 seconds.

Explanation / Answer

An open paint bucket of mass 12kg is attached to another paintbucket of mass 9kg by a light rope 21m long. The light bucket is atrest on the ground, and the rope goes up and over a smallfrictionless pulley and is attached to the heavy bucket. The heavybucket is on a window sill 11m above the top of the bucket on theground. There is no slack in the rope. If the heavy bucket slipsoff the window sill, how long will it be until the buckets collideand the first big splash occurs? This problem looks very easy and I did the problem, but I'mgetting a different answer. I keep checking but I don't know whereI'm doing wrong. The answer is supposed to be 2.8 seconds.
acceleration of the system ofbuckets=(m2-m1/m1+m2)g=(12-9/21)9.8=1.4m/sec2
time to cover (21-11)=10m can be calculated using h=ut+1/2at*t
so
11/2=0+(1.4/2)t*t=0.7t*t

so t=5.5/0.7=2.8sec

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