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A rifle with a muzzle velocity of [tex]V_0[/tex] shoots a bullet at a target [tex]R[/tex] away at the level of the muzzle. How high above the target must the rifle be aimed so that the bullet will hit the target? (Neglect air resistance.)

Let [tex]V_0 = 250 \, \text{m/s}[/tex] and [tex]R = 100 \, \text{m}[/tex]. Find [tex]H[/tex].

Answer :

Answer:

H = 0.784 m

Explanation:

given,

speed of velocity in x - direction = Vâ‚€

Range, R = 100 m

let time taken be t

in - x direction

[tex]R = V_x t[/tex]

[tex]R = V_0 t[/tex]

[tex]t = \dfrac{R}{V_0}[/tex]

in- y direction

[tex]H = V_{y}t+\dfrac{1}{2}gt^2[/tex]

[tex]H = 0+\dfrac{1}{2}gt^2[/tex]

[tex]H = \dfrac{1}{2}g(\dfrac{R}{V_0})^2[/tex]

[tex]H = \dfrac{gR^2}{2V_0^2}[/tex]

[tex]H = \dfrac{9.8\times 100^2}{2\times 250^2}[/tex]

H = 0.784 m

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Rewritten by : Jeany

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