Question

The initial speed of bullet fires from a rifle is 630m /s . The rifle is fired at the centre of a target 700m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target

Answer 1

Step 1: Given that:

Initial speed of the bullet = $630m{s}^{-1}$

The horizontal distance of the target from the position of the rifle = $700m$

Step 2: Calculation of the height up to which the rife must be aimed to hit the target:

There will be two components of the initial velocity of the bullet;

The horizontal component($u_h$) = $630m{s}^{-1}$

The vertical component($u_v$) = 0

( as the rifle is placed horizontally to the same level as the target.)

Now, let the time taken by the bullet to cover the distance of $700m$ is t then,

$t=\frac{Distance}{time}$

$t=\frac{700m}{630m{s}^{-1}}$

$t=1.11sec$

Now, The rifle must be aimed to a height h to hit the target, then

Using the second equation of motion under gravity for vertical motion;

$h=u_{v}t+\frac{1}{2}g{t}^2$

If g= $10m{s}^{-2}$

Putting all the values we get;

$h=0\times 1.11sec+\frac{1}{2}\times 10m{s}^{-2}\times {\left(1.11sec\right)}^2$

$h=5\times 1.23$

$h=6.15m$

$h=6.2m$

Thus,

The height up to which the rife must be aimed to hit the target will be 6.2m.