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A rifle is aimed horizontally at a target 51.0 m away. The bullet hits the target 1.60 cm below the aim point.  What was the bullet's speed as it left the barrel?

Question

A rifle is aimed horizontally at a target 51.0 m away. The bullet hits the target 1.60 cm below the aim point.  What was the bullet's speed as it left the barrel?

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Step 1

Given Information :

Target distance is Sx = 51 m

Bullet hits the target  1.6 cm bellow the aim point.

Sy = 1.6 cm  = 0.016 m

Motion of the bullet is as shown in the figure below.

16cm
51m
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16cm 51m

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Step 2

We can find the time taken by the bullet to travel 0.016 m in vertically downward direction as follows:

+at?
Sy
Acceleration in vertical direction = g 9.81 m/s2 (downwards)
Initial velocity in vertical direction u -0
0.016 (0)t(9.81)t2
(9.81)t?
0.016
Time t 0.05711 seconds
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+at? Sy Acceleration in vertical direction = g 9.81 m/s2 (downwards) Initial velocity in vertical direction u -0 0.016 (0)t(9.81)t2 (9.81)t? 0.016 Time t 0.05711 seconds

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Step 3

In this time interval (t = 0.05711 second) the distance travelled by ...

51 Vt
51 V(0.0571
Velocity of the bullet v = 893 m/s
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51 Vt 51 V(0.0571 Velocity of the bullet v = 893 m/s

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