A hunter is riding an elephant of height `4m` moving in straight line with uniform speed of `2m//sec`. A deer running with a speed `V` in fornt at a distance of `4sqrt(5)` moving perpendicular to the direction of motion of the elephant. If hunter can throw his spear with a speed of `10m//sec`. relative to the elephant, then at what angle `theta` to it's direction of motion must he throw his spear horizontally for a successful hit. Find also the speed 'V' of the deer.

Answer

`theta = 37^(@), v = 6m//s`

Explanation

spear is free falling along z-axis
`u = (1)/(2) "gt"^(2) rArr u = (10)/(2)t^(2) rArr t = (2)/(sqrt(5)) sec`
velocity of spear along x-axis to hit `= (10 cos theta +2)`

`(10 cos theta +2) xx (2)/(sqrt(5)) = 4sqrt(5) rArr 10 cos theta +2 = 10`
`rArr cos theta = (4)/(5) rArr theta = 37^(@)`
`{:("velocity of dear",,,rArrv=10sin theta,),(rArrv=10xx0.6,,,rArrv=6m//s,):}`