Question

A gun is used to shoot a target located at a distance of 100.0m. The gun is pointed horizontally at a height of 1.3 m above the ground. At the impact with the target, 78% of the kinetic energy of the bullet is absorbed by the target, and all vertical velocity is lost. The bullet rebounds hitting the shooter in the knee (between 50.0 and 50.2 cm above the ground). Calculate the initial velocity of the bullet with a 0.1 m/s precision. Neglect air resistance. The mass of the bullet is 4.2 g.

Please when solving write out the equations before using them.

Answer 1

Lets say bullet leaves the gun with velocity =

So, the Kinetic energy of the bullet before hitting the target =   _________relation 1

Since there is no loss of energy due to air resistance the Kinetic energy does not change till it hits the target.

After bullet hitting the target the target absorbs percent of its kinetic energy.

Just after hitting the target the bullet is left with the kinetic energy and it is given as

_____________________relation 2

let,

be the velocity of the bullet in the horizontal direction after rebounding from the target.

The   in terms of   is given as,

Using relation 2 we will have

Using relation 1 we will have

we will have relation between horizontal velocities before and after hitting the target as

  

that is

____________________________relation 3

Distance between Target and the shooter, .

After rebounding from the target since there is no air resistance the bullet will travel back with horizontal velocity

and after time   will hit the shooters knee.

so, we have

________________________________relation 4

In the same time bullet travels downward distance   under the effect of gravity with constant acceleration and hits the shooters Knee.

downward distance = Height of the gun height of the knee =

Lets say,

= Vertical velocity of the bullet just after hitting the target

we have

The relation between Downward distance , time ,constant acceleration , initial vertical velocity is given as fallowing kinematic relation,

Using values of and in above equation we get,

Using this value of in relation 4 we get

Using this value in relation 3 we get