# I lack the competence in basic physics

1. Aug 5, 2014

### CaptainUno

1. The problem statement, all variables and given/known data

A bike and its rider have a total mass of 86kg. If the rider is coasting on level ground at 9m/s and a 40N head wind acts on the rider for 12 seconds. What is the final velocity of the rider?

2. Relevant equations

3. The attempt at a solution
Assumption (Converting the Air resistance to velocity) : 40N x 12s = 480
480/86kg= 5.58m/s
9m/s - 5.58m/s = 3.42m/s is this correct or am I using the wrong equations

2. Aug 5, 2014

### Shinaolord

Looks correct to me.

$$\int_0^{12} 40 dt= 40*12=480$$ so we have
Next because the above is impulse, and impulse is equal to $$\Delta{p}$$ which is $$mv$$. Rearranging the equation $$480=m \Delta{v}$$

$$\frac{480}{mass} = \Delta{v}$$ where $$\Delta{v} = v_f-v_i$$

$$\Delta{v} = 9-\frac{480}{86} \approx 3.4$$

The paragraph below is incorrect.

[strike]Now we have the change in velocity. Subtract 5.6 from 9, which you did, and you should have the correct answer. [/strike]

NOtE: your problem has only 1 significant figure. So technically $$v_f \approx 3$$

Last edited: Aug 5, 2014
3. Aug 5, 2014

### Nathanael

(I'm assuming you know Momentum = mass*velocity)

Have you ever heard the following definition of force? "Force is change in momentum per (change in) time"
(in math: $F=\frac{ΔP}{Δt}=m\frac{Δv}{Δt}=ma$)

This means if you multiply the force by the time you will get the change in momentum
($40\cdot 12=480$)

Subtract that (because it's in the opposite direction) from the original momentum and you will have final momentum of the bike rider
(And then divide by the mass to get the final speed)

$\frac{9\cdot 86-480}{86}=9-\frac{480}{86}=3.42$

Your answer was correct but it's good to understand why what you did works.

Last edited: Aug 5, 2014
4. Aug 5, 2014

### Shinaolord

[strike]I believe 9-(480)/86 isn't 3.4. It's 5.6.[/strike]

But I like your explanation better than mine :)

Edit : nvm your math is correct

5. Aug 5, 2014

### Nathanael

So you're saying 480/86 is about 3.4? My calculator disagrees

6. Aug 5, 2014

### Shinaolord

Edited; I was wrong. I had done something wron in my first post. Apologies
I messed up with My calculator. somehow :0