A sharpshooter shoots the bullet horizontally over level ground with a velocity of 300m/s. At the instant that the bullet leaves the barrel, its empty shell casing falls vertically and strikes the ground with a vertical velocity of 5m/s.
How far does the bullet travel?
is 153m the correct answer?
The fall time of the bullet is
t = (5 m/s)/g = 0.510 s
If you assume the bullet does not slow down, it travels 300 m/s * 0.510 s = 153 m
So you are correct.
The bullet actually will slow down somewhat due to aerodynamic drag, but neglecting the drag on bullets is not a bad assumption.
drwls isn't quite right. Neglecting bullet drag is a very bad assumption because 1. Bullets are very light (they do most of their damage from speed, which increases kinetic energy exponentially) and 2. Drag affects fast objects exponentially more.
However, the question's theme allows us to neglect drag.
Find the solution at #4 here:
aquantaday.wordpress.com/grade-12-physics-challenge-problems-1-kinematics/
684 m is the correct answer if you do not account for drag.
My mistake, the answer is not 684 m in your case, my problem was the same but with speed changed. But you can sub your figure into my calculations to find the right answer, which is 153 m
To find how far the bullet travels horizontally, we need to analyze the motion of the bullet.
Given:
Initial horizontal velocity (Vx) = 300 m/s
Vertical velocity (Vy) = 0 m/s (since the bullet is shot horizontally)
Vertical acceleration (ay) = 9.8 m/s² (due to gravity)
Time taken for the bullet to hit the ground (t) = ?
Since the bullet is shot horizontally, its initial vertical velocity is zero. The only force acting on the bullet in the vertical direction is gravity, causing it to fall vertically. The time taken for the bullet to hit the ground vertically can be calculated using the equation:
t = (2 * Vy) / ay
Substituting the given values, we have:
t = (2 * 0 m/s) / 9.8 m/s² (since Vy = 0 m/s)
This simplifies to:
t = 0 second
Since the calculated time is zero, it indicates that the bullet hits the ground in an instant, without any vertical displacement.
Therefore, the bullet travels horizontally until it hits the ground without being affected by gravity. The horizontal distance traveled by the bullet can be calculated using the equation:
Distance = Velocity * Time
Since the time taken (t) is zero, the bullet does not take any time to hit the ground. Thus, the distance traveled by the bullet horizontally is always constant, and it is given by multiplying its horizontal velocity (Vx) with the time taken (t).
Distance traveled by the bullet = Vx * t
= 300 m/s * 0 s
= 0 meter
Therefore, the bullet does not travel any distance horizontally.