Ncert Exercises & Solutions

4.29 A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

NEETprep Answer:

G i v e n,

R = 3 k m

θ = 30^{0}

g = 9.8 m / s^{2}

W e k n o w t h a t,

R = \frac{u^{2} \sin 2 θ}{g}

\Rightarrow 3 = \frac{u^{2}}{g} \sin 60^{0}

\Rightarrow \frac{u^{2}}{g} = 2 \sqrt{3} . . . . . . (1)

I f, θ = 45^{0}

R_{m a x} = \frac{u^{2}}{g} . . . . . . (2)

O n c o m p a r i n g e q u a t i o n (1) a n d (2), w e g e t,

R_{m a x} = 2 \sqrt{3} = 2 \times 1.732 = 3.46 k m

T h e r e f o r e, t h e r e i s n o w a y w e c a n h i t t h e t a r g e t .

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