A boat is moving with a velocity $3i + 4j $ with respect to ground. The water in the river is moving with a velocity $-3i -4j $ with respect to ground. The relative velocity of the boat with respect to water is

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$......$

FIgure shows a sphere of mass $500\ g$ moving in a steady flow of air in the $x- $ direction. The  air-stream  exerts an essentially constant force of $0.9\  N$ on the sphere in the $x-$ direction. If at $t = 0$ the sphere is moving a s shown in the figure, determine the time required for the sphere to cross the $y-$ axis again  ........ $\sec$

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 $...........\frac{m}{s}$

Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the statement about their relative velocity $v_{12}$ is true?

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 with which man was running