9303753286127016 A bullet fired at an angle of 30 degree 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.

A bullet fired at an angle of 30 degree 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.

 Range R of the projectile R = 3km

Angle of projection, =30o

Acceleration due to gravity, g = 9.8m/s2

The horizontal range for the projection velocity, u0, is given by the relation:

R = uo2Sin2θ/g

3 = uo2Sin600/g

uo2/ g = 2√3 …….(i)

The maximum range (Rmax) is achieved by the bullet when it is fired at an angle of 45 with the horizontal, that is, Rmax = uo2/ g ….(ii)

On comparing equations (i) and (ii), we get:

Rmax = 2 × 1.732 = 3.46 km

Hence, the bullet will not hit a target 5 km away.

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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