An object thrown vertically upwards reaches a height of 500m. What was its initial velcoity? How long will the object take to come back to the Earth? Assume `g=10m//s^(2)`

Explanation

Given: Displacement `(s)=500m`
Gravitational acceleration `(g)=-10m//s^(2)`
Final velocity `(v)=0m//s`
To find: Initial velocity `(u)=?`
`t_("total")=?`
Formulae: `v^(2)=u^(2)+2gs, t_("total")=2t`
`v=u+"gt"`
`:.v,g` and s is given,
to find u we use 3rd equation
Solution: `v^(2)=u^(2)+2gs`
`0=u^(2)-10000`
`10000=u^(2)`
`u=100m//s`
Since, we have v,u and g to find t
we use 1st equation
`v=u+"gt"`
`0=100+(-10)xxt`
`10t=100`
`t=10s`
Time of ascent `=` Time of descent
`:.t_("total")=2xx10`
`:.t_("total")=20s`
Initial velocity was 100 m/s and time taken to come back to Earth is 20s.