# Calculating the velocity of a target and embedded projectile

1. Nov 25, 2015

### NewtonIsAmazing

1. The problem statement, all variables and given/known data
A projectile of mass 100g, moving at a speed of 400m/s, collides with a stationary wooden target of mass 1.5kg which is free to move. The projectile enters the wooden target on impact and remains embedded in it.

2. Relevant equations

a) calculate the velocity of the target and embedded projectile immediately after the impact

b) calculate the average force of the impact, if the duration of the collision was 0.10 seconds

c) calculate the respective accelerations of the projectile and the target during the impact

3. The attempt at a solution

Attempt at a)

(0.1kg x 400m/s) + (1.5kg x 0m/s) = (0.1kg + 1.5kg) x V

40 kg m/s = 1.6kg x V

V = (40 kg m/s) / 1.6 kg

V = 25 m/s

Attempt at b) (I'm a little unsure of this question)

So I used this equation: f=(v-u)/t

F = ( 25 m/s - 400 m/s)/ 0.10 seconds

F = -3750N

Attempt at c) (the answer to this question is dependent on on b) being correct)

F=ma

a=F/m

acceleration of projectile =3750N / 0.1kg
acceleration of projectile = 37500m/s^2

Acceleration of target= 3750N/1.5kg
Acceleration of target= 2500m/s^2

I just know I've done something wrong. Can someone please help me?

2. Nov 25, 2015

### jbriggs444

This looks fine. It is usually better to keep your equations in symbolic form while doing the algebra and only substitute numbers in at the end. It does not matter much when the equations are simple, but for more complex equations, you can more readily see simplifications. It's also usually less writing.

Where does the equation "f=(v-u)/t" come from? What are v and u? What are their units?
If you divide meters per second by seconds, what would the units for the result be?

3. Nov 25, 2015

### NewtonIsAmazing

I want to find the average force. V is the final velocity and U is the initial velocity. Their units are m/s

Question c) is dependent on question b) being correct.

Is question b) correct? if not, what have I done wrong?

4. Nov 25, 2015

### stockzahn

This is correct.

Have another look at the units of your calculation of the force - you missed something.

The calculations are basically correct, but the values you gained in b) are wrong. Plus: There's an easier way to calculate the acceleration without using the results from b). What's the definition of acceleration in kinematics (not dynamics)?

5. Nov 25, 2015

### NewtonIsAmazing

I'm not sure what I've missed

V = U + AT ?

6. Nov 25, 2015

### stockzahn

Write down the units of your equation without the actual values.

Try to solve for A, maybe you'll see the answer then.

7. Nov 25, 2015

### NewtonIsAmazing

N = (m/s - m/s)/s

Those are the units

a = (v - u)/t

a = (25 - 400)/0.1

a = - 2750 m/s^2 (for the projectile)

a = (25 - 0) / 0.1
a = 250m/s^2 (for the target)

is this correct?

8. Nov 25, 2015

### stockzahn

Does that seem correct to you? N = m/s2

Except for a small mistake in the calculus for the projectile, yes.

9. Nov 25, 2015

### NewtonIsAmazing

So which values should I plug into N = m/s^2?

What mistake did I make?

10. Nov 25, 2015

### stockzahn

What's the defintion of 1 N (force)? 1 N = 1 ...

(25 - 400) = ...

11. Nov 25, 2015

### NewtonIsAmazing

I'm not sure

So should it be 400-25 instead?

12. Nov 25, 2015

### stockzahn

I'm sure you find that within 30 seconds on the internet, if you don't know it.

No, the formula was correct, just the result was wrong.

13. Nov 25, 2015

### NewtonIsAmazing

So 1N = 1 kg metres per second squared?

So what exactly did I get wrong in the working out?

14. Nov 25, 2015

### stockzahn

Correct. Now try to use it for calculating b).

(25-400) = -375, not -275

15. Nov 25, 2015

### NewtonIsAmazing

Which kilogram should I use? The kg for the projectile or the target?

16. Nov 25, 2015

### jbriggs444

Which mass you should use depends on which acceleration you calculated. Which acceleration did you calculate?

17. Nov 25, 2015

### stockzahn

In your initial attempt you wanted to calculat the force with difference in movement of the projectile... If you continue with that you have to use the projectile's mass. But according to Newton's 3rd law you get the same result calculating the force with all data of the wood.

18. Nov 25, 2015

### NewtonIsAmazing

F=0.1kg(25m/s-400m/s)/0.1s
F=-375N

Is this the correct answer for b)?

19. Nov 25, 2015

### stockzahn

Yes, that's it.

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