A rifle is aimed horizontally toward the center of a target 110 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? (Ignore air friction. )

A) 21 m/s
B) 1,089 m/s
C) 30 m/s
D) 770 m/s
E) 385 m/s

Question

A rifle is aimed horizontally toward the center of a target 110 m away.If the bullet strikes 10 cm below the center,what was the velocity of the bullet? (Ignore air friction. )
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A) 21 m/s
B) 1,089 m/s
C) 30 m/s
D) 770 m/s
E) 385 m/s

Quizplus · Accepted Answer

We can use the equation of motion: 
y = vi*t + 0.5*a*t^2 
Since the initial vertical velocity is 0, the equation simplifies to: 
y = 0.5*a*t^2 
where y is the vertical displacement, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight. 
Since the rifle is aimed horizontally, the initial horizontal velocity (vx) remains constant throughout the motion, and can be found using the horizontal distance and time of flight: 
x = vx*t 
vx = x/t 
Substituting x = 110 m (distance to the target) and y = -0.1 m (10 cm below the center): 
vx = x/t = 110 m / t 
y = 0.5*a*t^2 = -0.1 m 
Solving for t: 
t = sqrt(2*y/a) = sqrt(2*0.1/9.8) = 0.143 s 
Substituting t back into the equation for vx: 
vx = 110 m / t = 110 m / 0.143 s = 770 m/s

A Rifle Is Aimed Horizontally Toward the Center of a Target