00:01
Here we have to find the acceleration in the direction of acceleration of a system shown here.
00:08
So there are two forces of 60 newtons and 40 neutons, and the angle between these two forces is 45 degrees.
00:15
First, let's find the acceleration.
00:19
Now let's write down the second newton's low, so f1 plus f2 equals to mass multiplied by the acceleration, all in vector 4.
00:30
So now we have to find the total force.
00:34
So to do it, we'll use the sum of these two vectors.
00:39
To calculate the vectors, to calculate the vector sum of two vectors, we have to build a figure to parallelogram.
00:47
And from this parallel, we need to calculate the diagonal.
00:52
So the diagonal, which is f total, we can find by using the cosine theorem.
01:00
So from the bottom triangle with the size of 40 and 16 newton's and f2 we can find f total we can find f total so f total equal squared equals to f1 squared plus f2 squared plus 2 multiplied by f1 multiply by f2 and multiply by the cosine between these two vectors so the cosine between f1 and f2 let's say this is f1 this is f2 is 180 minus 45 degree sorry here is the negative sign so therefore and therefore the mass sorry the acceleration of the object can be calculated as the total force multiply by the mass or which is square root of f1 squared plus f2 squared minus 2 multiply by f1 multiply by f2 by the cosine of 180 minus 45, which is 135, divided by mass.
02:20
So now let's complete this calculation.
03:02
So the acceleration of the boat, or sorry, the acceleration of the object equals to 33 .5 meters per second square.
03:12
Now we have to find the direction of this acceleration...