Bullet trajectory: Aiming a gun

[donaldparida]

Homework Statement

:
[/B]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 ?

Homework Equations

: [/B]
$H_{max}=\frac{u^2\sin^2\theta}{2g}$
$R=\frac{u^2\sin2\theta}{g}$
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?

 

[haruspex]

what height of the bird he should aim his gun to hit it ?

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

 

[donaldparida]

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

 

[haruspex]

@haruspex, Here is the diagram i drew while solving this problem,
View attachment 206195

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

 

[donaldparida]

@haruspex, here it is:

 

[haruspex]

@haruspex, here it is:
View attachment 206196

No, that is not the point the shooter would point her gun at.

 

[donaldparida]

@haruspex, Why?

 

[haruspex]

@haruspex, Why?

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?

 

[donaldparida]

The direction of $\vec{U}$?

 

[haruspex]

The direction of $\vec{U}$?

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