Question

An airplane travels 2100 km at 1000km/hE. It encounters a wind and slows to 800 km/h E for the next 1300 km. What is the average velocity of the airplane for this trip?

Answer 1

Answer:

The average velocity of the airplane for this trip is 1684.21 km/h

Explanation:

Average velocity is the rate of change of displacement with time. That is,

Average velocity = $\frac{Displacement }{Change in time}$ = Δx / Δt = $\frac{x2 - x1}{t2 - t1}$

Now we will calculate the time taken by the airplane for the first motion before it encounters a wind.

From,

Velocity = $\frac{Distance traveled}{Time taken}$

Time = $\frac{Distance traveled}{Velocity}$

Therefore, Time = $\frac{2100km }{1000km/h}$

Time = 2.1h

This is the time taken before the airplane encounters a wind.

Hence, t1 = 2.1h

Now, For the time taken by the airplane when it encounters a wind

Also from,

Velocity = $\frac{Distance traveled}{Time taken}$

Time = $\frac{Distance traveled}{Velocity}$

Therefore, Time = $\frac{1300km }{800km/h}$

Time = 1.625h

Hence, t2 = 1.625h

Now, to calculate the average velocity

Average velocity = $\frac{x2 - x1}{t2 - t1}$

x1= 2100, x2= 1300, t1= 2.1h and t2= 1.625h

Hence, Average velocity = $\frac{1300 - 2100}{1.625 - 2.1}$

Average velocity = 1684.21 km/h