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
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