An object slides down a slope of 15 m that makes 30 degrees with the horizontal at 2 m/s. What is the rate of change of its height. Is it constant.
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.