J J Science Academy - Practice Test

Subject: Physics

Topic: 4. Linear kinematics

SubTopic: 4.12 Relative Velocity

Test Type: NEET

Question 1: 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

$$& v=\sqrt{(24)^{2}+(7)^{2}}=25 m / s \\ & \alpha=\tan^{-1}\left(\frac{7}{24}\right)$$

Question 2: 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

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 $(= 30 min)$