# Solving 2D Jumping Motion Homework

In summary: I got -1.48m.In summary, a man jumps from one building to another with a running start and an angle of 14 degrees. To determine if he will make it to the other building, which is 1.1 meters shorter, his vertical displacement upon reaching the front edge of the lower building is calculated using the equations for displacement and horizontal displacement, taking into account the acceleration of gravity. The correct answer is -1.48 meters, with the possibility of slight variation due to rounding.

## Homework Statement

A man jumps from the top of a building to the top of another building 3.7 meters away. After a running start he leaps at an angle of 14 degrees with respect to the flat roof while traveling at a speed of 5.1 m/s. The acceleration of gravity is 9.81 m/s/s. To determine if he will make it to the other roof, which is 1.1 meters shorter than the building from which he jumps, find his vertical displacement upon reaching the front edge of the lower building with respect to the taller building.

## Homework Equations

y = v$$_{}oy$$t - (1/2)gt$$^{}2$$
x = v$$_{}ox$$t

## The Attempt at a Solution

3.7 = 5.1cos14t
t = 3.7/5.1cos14
y = 5.1sin14(.7) - (1/2)(9.81)(.7$$^{}2$$)
y = -1.54

The answer sounds reasonable - what could possibly be wrong?

I don't see anything wrong with your approach. I notice that you do a lot of rounding of numbers in between calculations. This will affect your final answer slightly. Also, have you taken into account that the 2nd building is 1.1m shorter than the 1st?

Just out of wonderment what answer did the book give you?

Merely glancing over your work and not solving it myself. I think one problem is your 51.sin14.7 part. If I am reading this right, the other roof is shorter than the roof you are on, since your displacement is downwards which means your velocity is downwards, which means it should be negative.

What should be negative? I gave the answer y = -1.54, and I actually have tried several other answers close to that. Also, I'm not using a textbook; I'm entering answers into an online homework service, so I don't know what the right answer is until I figure it out myself.

Any idea what specifically I should change?

What exactly do I need to do with the 1.1 difference in heights? If anything, I thought that would be the displacement.

## 1. What is 2D jumping motion?

2D jumping motion refers to the movement of an object in two dimensions, typically on a flat surface. In this type of motion, the object's position changes in both the horizontal and vertical directions as it moves through space.

## 2. How is 2D jumping motion different from 1D motion?

In 2D jumping motion, the object is moving in two perpendicular directions, whereas in 1D motion, the object is only moving in one direction. This means that in 2D jumping motion, we must consider both the horizontal and vertical components of the object's velocity and acceleration.

## 3. What equations are used to solve 2D jumping motion problems?

The equations used to solve 2D jumping motion problems depend on the specific scenario, but generally, we use the equations of motion (such as position, velocity, and acceleration) in both the horizontal and vertical directions, as well as the kinematic equations for projectile motion.

## 4. How do you find the initial velocity in 2D jumping motion?

To find the initial velocity in 2D jumping motion, we can use the formula v0 = √(vx02 + vy02), where vx0 and vy0 are the initial velocities in the horizontal and vertical directions, respectively.

## 5. Can air resistance affect 2D jumping motion?

Yes, air resistance can affect 2D jumping motion. In real-world scenarios, air resistance can cause objects to slow down and change direction while in motion. In order to accurately model 2D jumping motion with air resistance, we would need to use more complex equations and take into account factors such as the object's shape and air density.

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