# An object drops from a cliff that is 150m high. The distance, d, in metres that the object has dropped at `t` seconds is modelled by `d(t)=4.9(t)^(2)` - Find the rate at which the object hits...

An object drops from a cliff that is 150m high. The distance, d, in metres that the object has dropped at `t` seconds is modelled by `d(t)=4.9(t)^(2)`

- Find the rate at which the object hits the ground to the nearest tenth (answer should be in metres per second - m/s).

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### 1 Answer

If the distance that the object has dropped at t seconds is modeled by

`d(t) = 4.9t^2` , the rate is modeled by the derivative of this function:

`r(t) = (dd(t))/dt = 9.8t` . The units of the rate are m/s.

The time at which the object hits the ground can be calculating by letting d = 150 m:

`150 = 4.9t`

`t = 150/4.9 = 30.61s`

At this time, the rate will be `r = 9.8*30.61 = 300` m/s.

**The object hits the ground at the rate of 300 m/s.**