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?

1 Answer
Mar 17, 2018

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,enter image source here

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))