Two particles $A$ and $B$ start moving with velocities $20 \,m / s$ and $30 \sqrt{2} \,m / s$ along $x$-axis and at an angle $45^{\circ}$ with $x$-axis respectively in $x y$-plane from origin. The relative velocity of $B$ w.r.t. $A$ is ........... $m / s$
$(10 \hat{i}+30 \hat{j})$
$(30 \hat{i}+10 \hat{j})$
$(30 \hat{i}-20 \sqrt{2} \hat{j})$
$(30 \sqrt{2} \hat{i}+10 \sqrt{2} \hat{j})$
When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v,$ he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta) v ,$ this angle changes to $45^{\circ} .$ The value of $\beta$ is close to$......$
A river is flowing from east to west at a speed of $5\, m/min$ A man on south bank of river, capable of swimming $10\,m/min$ in still water, wants to swim across the river in shortest time. He should swim
A butterfly is flying with a velocity $4 \sqrt{2} \,{m} / {s}$ in North-East direction. Wind is slowly blowing at $1$ ${m} / {s}$ from North to South. The resultant displacement of the butterfly in $3\, seconds$ is $....\,{m}.$
A person running horizontally observes that rain is falling on his head vertically with speed $10\,m/s$. He stops and observes that rain is coming at an angle $30^o$ with vertical. Find the speed of rain w.r.t. ground
A $2\,m$ wide truck is moving with a uniform speed $v_0=8\,m / s$ along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed $v$ when the truck is $4 m$ away from him. The minimum value of $v$ so that he can cross the road safely is $...........\frac{m}{s}$