Question

A bullet fired at an angle of 30° with the horizontal hits the ground 3 km away. By
adjusting its angle of projection, can one hope to hit a target 5 km away? Assume the
muzzle speed to be fixed, and neglect air resistance.​

Answer 1

Horizontal range , R = 3km = 3000m

a/c to question, muzzle speed to be fixed.

Let muzzle speed is u m/s

Use formula of horizontal range,

R = u²sin2(30°)/g

3000 = u²sin60°/10

30000/(√3/2) = u²

u² = 60000/√3 = 20000√3m .....(1)

Now, horizontal range , R= u²sin2/g

Maximum value of sin2[\tex]\theta[/tex] = 1

So, maximum height can be possible , H =20000√3/10

= 2000√3

= 3464m = 3.464km

So the bullet can maximum hit a target 3.46 Km away. Hence, it's not possible to hit a target 5km away.