motion under gravity, speed, deceleration

[forgetyourself]

Please help if anyone can

 

a knife hits the ground at a speed of 40 m s-1. It penetrates the ground to a depth of 30 cm. Acceleration due to gravity is 9.81 m s-2. How can i find the deceleration of the knife.

 

I know the following equation might help;

 

 

 

 

speed = distance / time

 

acceleration = change in speed / time

 

 

 

 

I also know that the knifes speed initial speed when it hits the ground is 40 m s-1 and its final speed is 0 ms-1. So its change in speed is 40ms-1.

 

But I dont know how to find the time, and i dont know if i am using the correct equations for this question. Ive been reading my physics books for hours now but cannot figure it out.

 

I would really appreciate any help.

 

Can (Ek = 1/2 mv squared) help me?

 

 

 

 

 

[imatfaal]

You have to make an assumption about the rate of deceleration (ie the shape of the curve) as far as I can see.

Edited April 6, 2011 by imatfaal

[forgetyourself]

You have to make an assumption about the rate of deceleration (ie the shape of the curve) as far as I can see.

 

Thanks imatfaal. But im still stuck. How would i know the rate of deceleration of the knife penetrating the ground. Is it a constant?

 

Thanks!

[CaptainBlood]

First, since you know velocity solve v = v0 + at for time.  Then, use x = x0 + v0t + 1/2 at^2 solve this for acceleration and the figure out what it is considering the gravity is 9.8 m/s^2.

Edited April 7, 2011 by CaptainBlood

[imatfaal]

ForgYour

I would start with the assumption that deceleration is uniform - ie that velocity/time curve is straight line sloping to zero. You know the initial velocity, you know the final velocity, and you know the distance covered. Look through your equations of motion and you should be able to make progress. This Wikipedia page has the basic equations - but you might try first to remember.

As a final hint, you have v u s and need a (bear in mind you also have v² u²)

 

Captn

Not sure where you are going - you have too many variables to solve it that way v=u+at remember a is the deceleration due to hitting ground not acceleration due to gravity (or if you want to be really careful it is the sum of the two)

For extra credit you could consider other shapes of the velocity/time curve - what other factors would affect deceleration and investigate how you might find the deceleration at any point

[forgetyourself]

Hi Imat

Thank you so much for the tips . That's a great help to me. ill keep all your advice in minD when sit down to tackle this one again.

[CaptainBlood]

Right, v, v0 and x is all we have given, didn't really think this one through, sorry.