Question

A shell is fired vertically upwards with a velocity V1 from the Deck of a ship travelling at a speed of V to a person on the Shore observes the motion of the shell as parabola its horizontal range is given by?

Answer 1

Actually as the ship is moving horizontally with velocity `v` so when a shell is fired at velocity `v_1` vertically,it also proceeds with horizontal velocity `v` ,as seen by a person on the shore.

So,its trajectory looks like as follows,

Suppose,the height of the ship is `h`,so if the shell took time `t` to go to the water then,using `s=ut-1/2 g t^2`

we get,

`-h=v_1t -1/2 g t^2` (as,if the shell goes up by distance `x` then on reaching water its total displacement is `x-(x+h)=-h`)

so,`t=(2v_1+sqrt(4v_1 ^2 +8gh))/(2g)` (omited the negative value as, `2v+k>2v` so that would have given negative value of time)

So,in this time if it had gone distance `R` horizontally, then,

`R=vt=v((2v_1+sqrt(4v_1 ^2 +8gh))/(2g))`