a) Water only.
The force required to lift the water is the water's weight.
When the bucket is x metres off the ground, the expression for the water's weight can be found by first graphing it:
So, using y = mx + c, we see that the slope is
`m = -2/20 = -1/10` and
the y-intercept is `c = 2`
So we can write the function for the weight at height x as:
`F(x)=-x/10 + 2`
`=20 text[ N.m (20 joules)]`
Alternatively, we could have found the function as follows:
`F(x) = 2(20-x)/20 "N"`
where `2` is the original weight of the water, and `(20-x)/20` is the proportion of water left at height `t`.
This simplifies to `F(x)=(2-x/10)\ "N"`.
Easy to understand math videos: