Question

A rifle is aimed horizontally at a target 30m away. The bullet hits the target 2.9 cm below the aiming point. What is the bullet's speed ( in the unit of m/s) as it emerges from the rifle.

Answer 1

Speed of bullet = 389.61 m/s.

Step-by-step explanation:

Considering the vertical motion of bullet

Initial vertical speed = 0 m/s

Vertical displacement = 2.9 cm = 0.029 m

Vertical acceleration = 9.81 m/s²

Substituting in s = ut + 0.5at²

0.029 = 0 x t + 0.5 x 9.81 x t²

t = 0.077 s

So ball hits the target after 0.077 s.

Now considering the vertical motion of bullet

Time = 0.077 s

Horizontal displacement = 30 m

Horizontal acceleration = 0 m/s²

Substituting in s = ut + 0.5at²

30 = u x 0.077 + 0.5 x 0 x 0.077²

u = 389.61 m/s

Speed of bullet = 389.61 m/s.

Answer 2

390 m/s

Step-by-step explanation:

Let the horizontal speed be u.

Horizontal distance , x = 30 m

Vertical distance, y = 2.9 cm

Let time taken be t.

Use second equation of motion in vertical direction

H = uy × t + 1/2 gt^2

0.029 = 0.5 × 9.8 × t^2

t = 0.077 s

Horizontal distance = horizontal velocity × time

30 = u × 0.077

u = 390 m/s