# A stone is dropped from the upper observation deck of a tower, 350 m above the ground with initial velocity 8m/s downwards. How long does it take to reach the ground?Assume g = 9.8m/s^2 and give...

A stone is dropped from the upper observation deck of a tower, 350 m above the ground with initial velocity 8m/s downwards. How long does it take to reach the ground?

Assume g = 9.8m/s^2 and give your answer to 2 decimal places

### 1 Answer | Add Yours

The velocity function is given by

`v = 8 + 9.8t`

where `t` is time in seconds from when the stone is dropped.

The distance travelled by the stone `t` seconds after it is dropped is given by` `

`d = 9.8t + 1/2(9.8)t^2`

The stone hits the ground when `d=350`

ie, when `4.9t^2 + 9.8t -350 = 0`

To obtain `t`, solve this quadratic using the quadratic formula:

`t = (-9.8+-sqrt(9.8^2 + 4(4.9)(350)))/9.8 = -1 +- 8.510`

`t` is positive, ` `so **t=7.51s to 2dp**