A jet aeroplane travelling at the speed of 500 km/hr ejects its products of combusion at speed of 1500 km/hr relative to jet plane. What is the relative velocity of the latter with respect to an observer on the ground?

To determine the relative velocity of the products of combustion with respect to an observer on the ground, we need to consider both the speed of the jet airplane and the speed at which it ejects its combustion products. This involves understanding how relative velocities work in a straightforward manner.

Breaking Down the Problem

First, let’s clarify the speeds involved:

• The speed of the jet airplane: 500 km/hr
• The speed of the combustion products relative to the jet: 1500 km/hr

Next, we need to establish the direction of these speeds. Typically, when we talk about a jet airplane flying forward, we assume that both the airplane and the ejected products of combustion are moving in the same direction. Therefore, we can add the speeds together to find the total speed of the combustion products relative to the ground.

Calculating the Relative Velocity

To find the relative velocity of the combustion products with respect to an observer on the ground, we perform the following calculation:

Relative Velocity = Speed of Jet + Speed of Combustion Products

Substituting the values:

Relative Velocity = 500 km/hr + 1500 km/hr

This gives us:

Relative Velocity = 2000 km/hr

Understanding the Result

So, the combustion products are moving at a speed of 2000 km/hr relative to an observer on the ground. This means that if you were standing on the ground watching the jet, you would see the ejected products moving away from the jet at this combined speed.

Real-World Implications

This concept is crucial in various fields, such as aerodynamics and propulsion engineering. Understanding how velocities combine helps engineers design more efficient engines and predict the behavior of exhaust gases, which can affect everything from fuel efficiency to environmental impact.

In summary, by simply adding the speeds of the jet and the combustion products, we find that the relative velocity of the combustion products with respect to an observer on the ground is 2000 km/hr. This straightforward approach to relative motion is fundamental in physics and engineering.