Application of Integration to Motion Question - Year 12 math

[writer2019]

Hi Guys,
my Question is: an object is propelled vertically upwards with an initial velocity of 20m/s from the top of a cliff that is 300m high. consider the height relative to the bottom of the cliff.

a) find it's height after 5 seconds
b) what is the velocity of the object after 5 seconds
c) when does the object reach it's greatest height.

I am stuck on Question C the answer say it is 20/7 seconds. I am only get 2.04 seconds. can someone tell me where I am going wrong or what I can do to get 2.85 seconds for question C

My working:

 

[LCKurtz]

2.04 is correct. Not -2.04.

 

[Steven G]

The integral of 20 is NOT 20.

-22.5 + 300 is NOT 227.5
227.5 is about 75 away from 300, NOT 22.5 away!!!

If you subtract two things and get 0, that means their difference is 0, that is they are the same! So if 20-9.8t=0, then 9.8t = 20 and t = 20/9.8 = 2.04

What does 20-9.8t represent? You used this so you must know what it represents!