# Bullet trajectory: Aiming a gun

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1. Jun 28, 2017

### donaldparida

1. The problem statement, all variables and given/known data:
A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim his gun to hit it ?

2. Relevant equations:
$H_{max}=\frac{u^2\sin^2\theta}{2g}$
$R=\frac{u^2\sin2\theta}{g}$
3. The attempt at a solution:

Range= $R=\frac{u^2\sin2\theta}{g}$

$\implies \sin2\theta=\frac{Rg}{u^2}$

$\implies \sin2\theta=\frac{1}{250}$

$\implies 2\theta=\sin^{-1}(\frac{1}{250})$

$\implies \theta\approx 0.11$

Maximum height=$H=\frac{u^2sin^2\theta}{2g}$

$\implies H=0.04 m$

The correct answer is 20 m. Where have i gone wrong?

Last edited: Jun 28, 2017
2. Jun 28, 2017

### haruspex

That is not the same as the max height reached. Draw a diagram.

3. Jun 28, 2017

### donaldparida

@haruspex, Here is the diagram i drew while solving this problem,

4. Jun 28, 2017

### haruspex

Ok, so show on it the point above the bird that the person aims at.

5. Jun 28, 2017

### donaldparida

@haruspex, here it is:

6. Jun 28, 2017

### haruspex

7. Jun 28, 2017

### donaldparida

8. Jun 28, 2017

### haruspex

If you point a gun in a certain direction, in what direction do you expect the bullet to emerge from the muzzle? What direction is that in your diagram?

9. Jun 28, 2017

### donaldparida

The direction of $\vec{U}$?

10. Jun 28, 2017

### haruspex

Yes. So P is a point in that line and vertically above the bird.