Question

A bullet moving horizontally with a speed of 500 m/s strikes a sandbag and penetrate a distance of 10 cm. How long does it take to come to rest?

Answer 1

It takes 0.0004 seconds for the bullet to come to rest after penetrating the sandbag

Step-by-step explanation:

When only the distance (d) and initial velocity (u) are given, you can use the following kinematic equation to find the time (t) it takes for an object to come to rest:

`v^2=u^2+2ad`

Note:

v is the final velocity (which is 0 when the object comes to rest)

u is the initial velocity

a is the acceleration

d is the distance

We can eliminate
`v` from the equation because it is 0.

`0^2=u^2+2ad`

Now lets isolate
`a`

`0^2=u^2+2ad\\\\`

`-2ad=u^2`

`a=-(u^2)/(2d)`

Now, you can use the acceleration to find the time (t) it takes for the object to come to rest using the equation:

`v=u+at`

Since v=0, the equation becomes:

`0=u+at`

Solving for t:

`t=-(u)/(a)`

Substituting our first expression for
`a` into the equation gives us:

`t=-(u)/(-(u^2)/(2d) )`

`t=-u*(2d)/(u^2)`

`t=(2d)/(u)`

Our distance is in centimeters. To convert to meters divide by 100.

`d=0.1\\u=500`

`t=(2*0.1)/(500)`

`t=(0.2)/(500)`

`t=0.0004`