# Solve 2 Equations 2 Unknowns: Hibbeler Dynamics 12th Ed.

• Mr Beatnik
In summary, the problem involves a skier leaving a ramp at an angle of 25 degrees and striking the ground at a point 100m down the slope. Using equations s=vt and s=s+vt+1/2at^2, the skier's initial speed,V, and time of flight,t, can be determined. The problem is 12-110 from the Hibbeler Dynamics 12th edition. After setting up the equations as (1) 100(4/5)=Vcos(25)t and (2) -4-100(3/5)=0+Vsin(25)t+(1/2)(-9.81)t^2, the correct solutions of V=19.
Mr Beatnik

## Homework Statement

Ok forgive me as an engineering student but this problem should be easier than it seems. The Problem: It is observed that the skier leaves the ramp A at an angle (Theata=25 degrees) with the horizontal. If he strikes the ground at point B, determine his initial speed,V, and the time of flight,t.

## Homework Equations

I have used:

s=vt
s=s+vt+1/2at^2

The dimensions needed are correct and are 100m down the slope alligned, the ramp he leaves from is 4m high and the ramp is angled at a 3,4,5 triangle.

This problem is 12-110 from the Hibbeler Dynamics 12th edition

## The Attempt at a Solution

I have setup the equations as

(1) 100(4/5)=Vcos(25)t
(2) -4-100(3/5)=0+Vsin(25)t+(1/2)(-9.81)t^2

I have tried solving (1) for t and plugging in into (2) but come out with a strange decimal and also solving (1) for V and plugging into (2) I can't seem to get it.

I know the answers are supposed to be: V=19.4m/s t=4.54s

Mr Beatnik said:

## Homework Statement

Ok forgive me as an engineering student but this problem should be easier than it seems. The Problem: It is observed that the skier leaves the ramp A at an angle (Theata=25 degrees) with the horizontal. If he strikes the ground at point B, determine his initial speed,V, and the time of flight,t.

## Homework Equations

I have used:

s=vt
s=s+vt+1/2at^2

The dimensions needed are correct and are 100m down the slope alligned, the ramp he leaves from is 4m high and the ramp is angled at a 3,4,5 triangle.

This problem is 12-110 from the Hibbeler Dynamics 12th edition

## The Attempt at a Solution

I have setup the equations as

(1) 100(4/5)=Vcos(25)t
(2) -4-100(3/5)=0+Vsin(25)t+(1/2)(-9.81)t^2

I have tried solving (1) for t and plugging in into (2) but come out with a strange decimal and also solving (1) for V and plugging into (2) I can't seem to get it.

I know the answers are supposed to be: V=19.4m/s t=4.54s

A 3-4-5 right triangle does not give you a takeoff angle of 25 degrees.

Sorry about the confusion and I am aware that a 3-4-5 triangle does not make a 25 degree takeoff. Here is a free body diagram to help describe. The equations are correct btw, I just can't solve the system. Thanks for the help.

#### Attachments

• Free Body Diagram.JPG
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Mr Beatnik said:
Sorry about the confusion and I am aware that a 3-4-5 triangle does not make a 25 degree takeoff. Here is a free body diagram to help describe. The equations are correct btw, I just can't solve the system. Thanks for the help.

Ah, that helps. Where did the "-4" come from?

(2) -4-100(3/5)=0+Vsin(25)t+(1/2)(-9.81)t^2

EDIT -- Oh wait, I see the ramp 4m offset in the figure now.

Last edited:
So as you said, you have two equations and two unknowns. How can you go about solving for V and t?

$$100(\frac{4}{5})=Vcos(25)t$$
$$-4-100(\frac{3}{5})=0+Vsin(25)t+(1/2)(-9.81)t^2$$

Yeah I need to solve for V and t.

Mr Beatnik said:
Yeah I need to solve for V and t.

So have at it! What would be a good way to start?

? I just ran through it again and it worked out. Unbelievable. I guess what thy say about walking away from the problem and coming back to it later really works. I am going to post my work. Thanks for your help.

Great! Good job.

Here is the work. It's a bit sloppy because I ran through it. Please excuse the mess.

#### Attachments

• My Work.jpg
15.2 KB · Views: 1,488

## 1. How do I solve 2 equations with 2 unknowns using the Hibbeler Dynamics 12th Edition?

To solve 2 equations with 2 unknowns using the Hibbeler Dynamics 12th Edition, you will need to use the method of substitution or elimination. Both methods involve manipulating the equations to isolate one variable and then substituting it into the other equation to solve for the other variable.

## 2. What are the steps to solve a system of 2 equations with 2 unknowns?

The steps to solve a system of 2 equations with 2 unknowns are as follows:

1. Identify the variables in each equation
2. Choose a method (substitution or elimination) to solve the system
3. Manipulate the equations to isolate one variable
4. Substitute the isolated variable into the other equation to solve for the other variable
5. Check your solution by plugging it back into the original equations

## 3. Can the Hibbeler Dynamics 12th Edition be used to solve systems of equations with more than 2 unknowns?

No, the Hibbeler Dynamics 12th Edition is specifically designed for solving systems of 2 equations with 2 unknowns. It may not be applicable for systems with more than 2 unknowns.

## 4. How accurate are the solutions obtained from using the Hibbeler Dynamics 12th Edition to solve equations?

The accuracy of the solutions obtained from using the Hibbeler Dynamics 12th Edition to solve equations depends on the accuracy of the given equations and the method used to solve them. It is important to double check the solution and make sure it satisfies both equations to ensure accuracy.

## 5. Are there any tips or tricks for solving systems of 2 equations with 2 unknowns using the Hibbeler Dynamics 12th Edition?

One tip for solving systems of 2 equations with 2 unknowns using the Hibbeler Dynamics 12th Edition is to use the elimination method if one of the equations has a coefficient of 1 for one of the variables. This will make the substitution process easier and may result in simpler solutions. Additionally, it is always helpful to double check your solution by plugging it back into the original equations.

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