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$......$
$0.41$
$0.50$
$0.37$
$0.73$
A boat covers certain distance between two spots in a river taking $t_1$ hrs going downstream and $t_2$ hrs going upstream. What time will be taken by boat to cover same distance in still water?
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 particle $(A)$ moves due north at $3\,km / h$ another particle $(B)$ due west at $4\,km / h$. The relative velocity of $A$ with respect to $B$ is $\left(\tan 37^{\circ}=3 / 4\right)$
Wind is blowing in the north direction at speed of $2 \,\,m/s$ which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him :
A boat crossing a river moves with a velocity $v$ relative to still water. The river is flowing with a velocity $v / 2$ with respect to the bank. The angle with respect to the flow direction with which the boat should move to minimize the drift is