A person sees an object on a tree at a heitht of ` 40 m` and at a distance of ` 60 m` . Whith what velocity he showld throw an arrow at an angle of `45^@` so that it may hit the object ? Take ` g= 10 ms^(2)`.

Explanation

Here, ` y= 40 m, x = 60 m, u= ? Theta = 45^2`
Let the arrow hit the object on tree in time (t),
Then ` x=u_x t+ 1/2 a_xt^2`
:.` 60 = u cos 45^2 t + 1/2 xx 0 t^2 = u xx 1/ (sqrt2)t`
or ` u = ( 60 sqrt2)/t` …(i)
` y=u_y t + 1/2 a-y t^2`
` 40= ( u sin 45^2) t- 1/2 gt^2`
`= u xx 1/( sqrt2) t - 1/2 gt^2`
or ` 40 = ( 60sqrt 2)/t xx 1/(sqrt2) t- 1/2 xx 10 t^@` [From (i)]`
or ` 5 t^2 = 60 - 40 =20 ` or ` t^2 = 4 ` or ` t= 2 s`
From (i), ` u = (60 sqrt2)/2 = 30 sqrt2 ms^(-1)`.