00:02
So interestingly, remember, m1 is given as 1 .25 kg, right? m2 is also given as 5 .95 kg, right? u is given as 3 .77 m per second, right? and h1 is given as 0 .126 m.
00:23
So therefore, for the first part, we need to use the law of conservation of momentum, where m1jh plus, of course, 1 .5 of m1u squared, right? let's give you 1 .5 of m1v1 squared, ok? so therefore, 1 .25 multiply 9 .8 multiply 0 .126 plus 0 .5 multiply by 1 .25 multiply that by 3 .77 squared must give you 0 .5 into 1 .25 and v1 squared, which means that if you do these calculations, you'll have 1 .5 435 plus 8 .88 3 must give you 0 .625 v squared, right? so v, therefore, will be equal to the square root of 1 .5 435 plus 8 .883 divided by 0 .625, and you have approximately 4 .08 meters per second, right? now moving on to part b of the question, remember that v1f should be equal to m1 minus m2, right? over m1 plus m2 multiply by v1, right? so therefore, we are looking at 1 .25 minus 5 .95 over 1 .25 plus 5 .95 multiply v1, which is basically 4 .08.
02:41
And these are minus 2 .66 meters per second.
02:48
But see, this negative sign shows that the direction is opposite to the original, ok? let me put it here, opposite direction to the original, right? and v2, final, therefore, must be equal to 2 multiplied by m1 v1, remember, over the combination of these masses, ok? so we're looking at 2 multiply 1 .25 and 4 .08 divided by 1 .25 plus 5 .95, and you have 1 .42 meters per second...