Answer:
dr/dt = 1.94 units per second
Explanation:
A particle is moving on the x-axis to the right at 2 u/s.
To know how is changing the distance of the particle respect to the point (0,9), on the y-axis, you first take into account that the distance between charge and a point over the y-axis is given by:
(1)
Next, you calculate implicitly the derivative of the equation (1) respect to t:
(2)
Next, you solve the previous equation for dr/dx:
(3)
dx/dt: the speed of the particle on the x-axis = 2
dy/dt: speed of the particle on the y-axis = 0
For the instant given in the statement, you have that:
x = 5
y = 9
Then, you replace the values for x, y, dx/dt and dy/dt in the equation (3):
The speed of change of the distance between particle and point (0,9) is 1.94 units per second