# 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.

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### 2 Answers

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.**