Q1. An aeroplane is moving relative to air with a speed of (24 m / s) towards north. If there is a wind blowing from west to east at a speed of (7 m / s) with respect to earth, the velocity of the aeroplane with respect to the earth is
1) (25 m / s) at (\tan^{-1}(7 / 24)) with north
2) (25 m / s) at (\tan^{-1}(7 / 24)) with east
3) (25 m / s) at (\tan^{-1}(24 / 7)) with north
4) (25 m / s) at (\tan^{-1}(24 / 7)) with east
Hint: $$& v=\sqrt{(24)^{2}+(7)^{2}}=25 m / s \\ & \alpha=\tan^{-1}\left(\frac{7}{24}\right)$$
Q2. A boat moves with a speed of (5 km / h) relative to water in a river flowing with a speed of (3 km / h) and having a width of 1 km . The minimum time taken around a round trip is
1) 5 min
2) 60 min
3) 20 min
4) 30 min
Hint: For the round trip he should cross perpendicular to the river. Time for trip to that side
$$t=\frac{1 km}{4 km / hr}=0.25 hr=15 min$$
To come back, again he take 15 min to cross the river. Total time
(= 30 min)