Two planes approach each other head-on. Each has a speed of 780 km/h, and they spot each other when they are initially 10.0 km apart. In how much time do the pilots have to take evasive action?

Short Answer

Expert verified

The time taken by the pilots to take evasive action is 23.1s.

Step by step solution

01

Step 1. Definition of relative velocity 

Relative velocity may be defined as the velocity of one particle relative to another particle. It involves the addition and subtraction of the velocity vectors.

02

Step 2. Given information

The velocity of the first plane is v1=780km/h.

The velocity of the second plane is v2=780km/h.

The distance is Δd=10km.

03

Step 3. Calculate the relative velocity between the two planes

As the two planes are approaching each other with the same velocity, the relative velocity between the two planes is equal to the sum of the two velocities of planes. Thus,

v=v1+v2v=(780km/h)+(780km/h)v=1560km/h

04

Step 4. Calculate the time taken by the pilots to take evasive action

The time taken by the pilots to take evasive action can be calculated as

t=Δdvt=(10km)(1560km/h)3600s1ht=23.1s

Thus, the time taken by the pilots to take evasive action is 23.1s.

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