Projectile Motion - Problem 16 - Kinematics of Particles - Engineering Mechanics

TL;DR

This analysis explains how to calculate the percentage increase in the range of a projectile when the initial velocity is increased by five percent.

Transcript

hi friends solve problem on projectile motion let's see what is given in problem by what percentage the range of projectile is increase if initial velocity is increased by five percent here nothing is given that means initial velocity is not given angle of projection is not given what will be the angle of projection we'll take here that angle remai... Read More

Key Insights

• 🧡 The problem involves finding the percentage increase in the range of a projectile when the initial velocity is increased by five percent.
• 🧡 The range of a projectile is determined by a formula that includes the initial velocity, angle of projection, and a constant value.
• 🧡 By substituting the new velocity in the range formula, the new range can be calculated and the percentage increase can be determined.
• 🔺 The angle of projection and other variables remain constant in this problem.
• 👶 The new velocity is calculated by adding five percent of the initial velocity to the initial velocity.
• 🧡 The percentage increase in the range is calculated by comparing the new range to the original range.
• 🍉 The cancellation of terms in the calculation simplifies the equation.

Questions & Answers

Q: What is the problem being analyzed in this content?

The problem involves calculating the percentage increase in the range of a projectile when the initial velocity is increased by five percent.

Q: What formula is used to determine the range of a projectile?

The range of a projectile is determined by the formula r = u0^2 * cos(2θ0) / g, where r is the range, u0 is the initial velocity, θ0 is the angle of projection, and g is a constant value.

Q: How is the new velocity calculated when the initial velocity is increased by five percent?

The new velocity, u0', is calculated by adding five percent of the initial velocity, u0, to the initial velocity: u0' = u0 + (0.05 * u0) = 1.05 * u0.

Q: How is the percentage increase in the range calculated?

The percentage increase in the range is calculated using the formula: (r' - r) / r * 100, where r' is the new range and r is the original range. In this case, the percentage increase is found to be 10.25 percent.

Summary & Key Takeaways

• The problem involves finding the percentage increase in the range of a projectile when the initial velocity is increased by five percent.

• The range of a projectile is given by a formula that includes the initial velocity, angle of projection, and a constant value.

• By substituting the new velocity in the range formula, the new range can be calculated and the percentage increase can be determined.