Question

The water from a fire hose follows a path described by y equals 3.0 plus 0.8 x minus 0.40 x squared ​(units are in​ meters). If v Subscript x is constant at 5.0 ​m/s, find the resultant velocity at the point left parenthesis 2.0 comma 3.0 right parenthesis .

Answer 1

Step-by-step explanation:

It is given that, the water from a fire hose follows a path described by equation :

`y=3+0.8x-0.4x^2`........(1)

The x component of constant velocity,
`v_x=5\ m/s`

We need to find the resultant velocity at the point (2,3).

Let
`(dx)/(dt)=v_x` and
`(dy)/(dt)=v_y`

Differentiating equation (1) wrt t as,

`(dy)/(dt)=0.8* (dx)/(dt)-0.8x* (dx)/(dt)`

`v_y=0.8* v_x-0.8x* v_x`

`v_y=0.8v_x(1-x)`

When x = 2 and
`v_x=5\ m/s`

So,

`v_y=0.8* 5* (1-2)`

`v_y=-4\ m/s`

Resultant velocity,
`v=√(v_x^2+v_y^2)`

`v=√(5^2+(-4)^2)`

v = 6.4 m/s

So, the resultant velocity at point (2,3) is 6.4 m/s. Hence, this is the required solution.