Question:

A jet airplane travelling at the speed of $ 500 \,km \,h^{-1} $ ejects its products of combustion at the speed of $ 1500 \,km\, h^{-1} $ relative to the jet plane. The speed of the products of combustion with respect to an observer on the ground is

Updated On: Jul 5, 2022
  • $ 500 \,km\, h^{-1} $
  • $ 1000 \,km\, h^{-1} $
  • $ 1500 \,km\, h^{-1} $
  • $ 2000 \,km\, h^{-1} $
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The Correct Option is B

Solution and Explanation

Velocity of jet plane w.r.t. ground
$ v_{JG} = 500 \,km\, h^{-1} $ Velocity of products of combustion w.r.t. jet plane $ v_{CJ} = - 1500\, km \,h^{-1} $ $ \therefore $ Velocity of products of combustion w.r.t. ground is $ v_{CG}=v_{CJ}+v_{JG}=-1500\,km\,h^{-1}+500\,km\,h^{-1} $ $ =-1000\,km\,h^{-1} $ $ -ve $ sign shows that the direction of products of combustion is opposite to that of the plane. $ \therefore $ Speed of the products of combustion w.r.t. ground $ = 1000\, km \,h^{-1} $ .
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Concepts Used:

Motion in a straight line

The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion. 

Types of Linear Motion:

Linear motion is also known as the Rectilinear Motion which are of two types:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.