A rifle is aimed horizontally at a target 50m away. The bullet hits the target 2.0cm below the aim point.
A. What was the bullet's fight time?
B. What was the bullet's speed as it left the barrel?
The bullet fell .02m.
heightfell=1/2 g t^2 find time
speed=50m/time
To find the answers to these questions, we can use the equations of motion for a projectile. Let's break down the problem step by step.
A. What was the bullet's flight time?
To find the flight time, we need to consider the vertical motion of the bullet. The bullet starts at the horizontal level of the aim point and hits the target 2.0cm below it. We can use the equation for vertical displacement to find the flight time.
The equation for vertical displacement is:
d = vit + (1/2)gt^2
Where:
d = vertical displacement (negative since the bullet hits below the aim point)
vi = initial vertical velocity (which is zero since the bullet is fired horizontally)
g = acceleration due to gravity (-9.8 m/s^2)
t = flight time (what we're trying to find)
Substituting the given values into the equation, we have:
-0.02m = 0 + (1/2)(-9.8m/s^2)t^2
Simplifying the equation, we get:
-0.02m = -4.9m/s^2 * t^2
Multiplying both sides by -1 to get rid of the negative signs, we have:
0.02m = 4.9m/s^2 * t^2
Dividing both sides by 4.9m/s^2, we get:
0.02m / 4.9m/s^2 = t^2
Simplifying further, we have:
0.00408163265 s^2 = t^2
Taking the square root of both sides, we get:
t ≈ 0.0638 seconds
So, the bullet's flight time was approximately 0.0638 seconds.
B. What was the bullet's speed as it left the barrel?
To find the speed of the bullet, we can use the horizontal motion of the bullet. Since there are no horizontal forces acting on the bullet (assuming no air resistance), the horizontal velocity remains constant throughout the motion. We can use the equation for horizontal displacement to find the speed.
The equation for horizontal displacement is:
d = v*t
Where:
d = horizontal displacement (50m)
v = horizontal velocity (what we're trying to find)
t = flight time (0.0638 seconds)
Substituting the given values into the equation, we have:
50m = v * 0.0638s
Simplifying the equation, we get:
v ≈ 784.96 m/s
So, the bullet's speed as it left the barrel was approximately 784.96 m/s.