The object slides down the slope of 15m that makes an angle of 30 degrees with the horizontal at a rate 2 m/s. If the height of the object when it slides down x m down the slope is h, sin 30 = `h/(15 - x)` .
h = (15 - x)*sin 30
`(dh)/dt = -sin 30*((dx)/dt)`
As the object slides down at 2 m/s, the height decreases at 2*sin 30 = 1 m/s. This is constant.
The height of the object decreases at a constant rate of 1 m/s.
The velocity along the incline is 2m/s (constant).
The velocity of the object in the vertical direction = 2.sin(30) = 1 m/s
The velocity is the rate of chage of distance and in the vertical direction it is the rate of change of height.
The rate of change of height is 1m/s and is constant.