Question

Good day I have two questions I need help ASAP.

A car travels 40.0km in 30 minutes then 80.0 km in 40 what is the resultant displacement,avaerage speed and average velocity?

An airplane flies south at the speed of 50 ms in still air what is the resultant velocity of the airplane if the wind is blowing east at 10ms ?

Answer 1

(i) resultant displacement: 40.0 km + 80/0 km = 120.0 km

average speed:

$$v = {d \over t} = {120.0 km \over 70 min} = 1.7km/min$$

average velocity: in this case they will be equal in absolute value with an average speed $\bar{v} = |v| = |1.7|$

(ii) when the aircraft moves, its speed relative to the earth is equal to the sum of the speeds of the aircraft relative to the speed of stationary air and wind speed:

$$\bar{v} = \bar{v_0} + \bar{u}$$

If the plane flies from the east, and the wind blows south, then:

$$v = \sqrt{\smash[b]{v_o^2 - u^2}} = \sqrt{\smash[b]{50^2 - 10^2}} = \sqrt{\smash[b]{2400}} \approx 49.99 m/s \approx 50 m/s$$