Question

From a motorboat moving downstream with a velocity $2m/s$ with respect to river, a stone is thrown. The stone falls on an ordinary boat at the instant when the motorboat collides with the ordinary boat. The velocity of the ordinary boat with respect to the river is equal to zero. The river flow velocity is given to be $1m/s$. The initial velocity vector of the stone with respect to earth is

• A. $2\hat{i}+20\hat{j}$
• B. $3\hat{i}+40\hat{j}$
• C. $3\hat{i}+50\hat{j}$
• D. $2\hat{i}+50\hat{j}$

Answer 1

The correct option is C $3\hat{i}+50\hat{j}$

Ref. image I

$\frac{d}{t}=\frac{20}{t}=2$

$\therefore t=10sec$

Ref. image II

$S=ut+\frac{1}{2}a{t}^2$

$0=u_{y}t+\frac{1}{2}(-g)t^2$

$\frac{1}{2}g{t}^2=u_{y}t$

$\therefore u_y=\frac{1}{2}\times 10\times 10=50m/s$

Ref. image III

$u_B-u_r=0$

$u_B=u_r$

$u_B=1m/s$

w.rt. river $2m/s$ V

$\to$

$4x=3m/s=2m/s+u_B$

$V_{store}=3\hat{i}+50\hat{j}$

Hence, option C is correct