The water from a fire hose follows a path described by y=5.0+0.9x-0.30x^2 (units are in meters). If vx is constant at 10.0 m/s, find the resultant velocity at the point (3.0,5.0).

Question

Find the magnitude of the velocity of the water at the point (3.0,5.0).

The magnitude is approximately ____.

(Type an integer or decimal rounded to one decimal place as​ needed.)

Answer 1

Let me take a shot at this.

So I'm assuming we are given velocity in the x direction: v_x, which is dx/dt

What we are looking for is velocity in the y direction, v_y, at points (3,5)

We also have y = 5.0 + 0.9x - 0.30x²

We will do the derivative in terms of time, t, because we are talking about position and velocity

dy/dt = d(5.0)/dt + d(0.9x)/dt - d(0.30x²)/dt

dy/dt = 0 + 0.9(dx/dt) - 0.30(dx²/dt)

v_y= 0.9v_x - (2)(0.30)(x)(dx/dt)

v_y = 0.9v_x - 0.60(x)(v_x)

v_y = 0.9(10) - 0.60(3.0)(10)

v_y = 9 - 18

v_y = -9 m/s

I hope this is correct!