(16) Say, a guy dumped by his (only) girlfriend. He wants to jump off from a building of 240 ft. high. What is the required velocity that he must start to touch down on her new boyfriend who stands on the ground, 40 ft. from the building? If a) the guy jumped out horizontally. b) the guy jumped with a depression angle of 20 degrees (the angle of depression is the angle between the horizontal line of look down sight to the object) In both cases find the impact velocities and speeds (Discuss the feasibility of the problem)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Problem Statement:**

A man, after being dumped by his girlfriend, is considering jumping off a building 240 feet high. He aims to land on the new boyfriend, who is standing 40 feet away from the base of the building. The goal is to calculate the initial velocity needed for this action under two scenarios:

a) The man jumps out *horizontally*.

b) The man jumps out with a *depression angle of 20 degrees*. The angle of depression is defined as the angle between the horizontal line and the line of sight down to the object.

**Task:**

For both scenarios, calculate the impact velocities and speeds. Additionally, discuss whether this problem is feasible.

**Analysis:**

1. **Horizontal Jump:**
   - Calculate the required horizontal velocity for the man to cover the distance of 40 feet while falling from a height of 240 feet.

2. **Jump with Depression Angle:**
   - Calculate the required velocity when jumping at a 20-degree angle downward.
   - Consider vertical and horizontal components of velocity due to the angle.

**Discussion:**
Evaluate the practicality and physical viability of the scenarios described. Would such a jump be possible given physical constraints and real-world physics?
Transcribed Image Text:**Problem Statement:** A man, after being dumped by his girlfriend, is considering jumping off a building 240 feet high. He aims to land on the new boyfriend, who is standing 40 feet away from the base of the building. The goal is to calculate the initial velocity needed for this action under two scenarios: a) The man jumps out *horizontally*. b) The man jumps out with a *depression angle of 20 degrees*. The angle of depression is defined as the angle between the horizontal line and the line of sight down to the object. **Task:** For both scenarios, calculate the impact velocities and speeds. Additionally, discuss whether this problem is feasible. **Analysis:** 1. **Horizontal Jump:** - Calculate the required horizontal velocity for the man to cover the distance of 40 feet while falling from a height of 240 feet. 2. **Jump with Depression Angle:** - Calculate the required velocity when jumping at a 20-degree angle downward. - Consider vertical and horizontal components of velocity due to the angle. **Discussion:** Evaluate the practicality and physical viability of the scenarios described. Would such a jump be possible given physical constraints and real-world physics?
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