Question

A hunter aims his gun at an apple on the top of a tree 40m high and at a distance of 60m from him. With what velocity the hunter should fire a bullet at an angle of 45° so that it may hit the apple.
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Answer 1

Given:

A hunter aims his gun at an apple on the top of a tree 40m high and at a distance of 60m from him.

To find:

Velocity the hunter should fire a bullet at an angle of 45° so that it may hit the apple.

Calculation:

This is an example of Ground-Air Projectile.

The general equation for trajectory is:

$\rm{y = x \tan( \theta) - \dfrac{g {x}^{2} }{2 {u}^{2} { \cos}^{2} ( \theta) }}$

Putting available values:

$= > \rm{y = x \tan( {45}^{ \circ} ) - \dfrac{g {x}^{2} }{2 {u}^{2} { \cos}^{2} ( {45}^{ \circ} ) }}$

$= > \rm{40 = 60 \tan( {45}^{ \circ} ) - \dfrac{g {(60)}^{2} }{2 {u}^{2} { \cos}^{2} ( {45}^{ \circ} ) }}$

$= > \rm{40 = 60 - \dfrac{g {(60)}^{2} }{2 {u}^{2} (\frac{1}{2} )}}$

$= > \rm{40 = 60 - \dfrac{3600g }{ {u}^{2} }}$

$= > \rm{ \dfrac{3600g }{ {u}^{2} } = 20}$

$= > \rm{ {u}^{2} = \dfrac{36000}{20} }$

$= > \rm{ {u}^{2} = 1800 }$

$= > \rm{ u = 42.42 \: m {s}^{ - 1} }$

So, final answer is:

$\boxed{\bf{ u = 42.42 \: m {s}^{ - 1} }}$