A bullet fired in a horizontal direction with muzzle velocity 300m/s. In the absence of air resistance,
a) how far will it have dropped in travelling a distance of 20m.
b) how far will it have dropped in one second
To answer these questions, we need to make use of the equations of motion. Let's break down the problem step by step.
a) How far will the bullet have dropped in traveling a distance of 20m?
To find the vertical displacement (the distance the bullet has dropped), we need to calculate the time it takes for the bullet to cover the given horizontal distance and then use this time to determine the vertical displacement using the equation of motion for vertical motion.
Step 1: Calculate the time taken to cover the horizontal distance of 20m.
We can use the formula: time = distance / velocity
time = 20m / 300m/s
time = 1/15 s
Step 2: Calculate the vertical displacement using the equation of motion.
The equation for vertical motion is: displacement = (initial velocity x time) + (0.5 x acceleration x time^2)
Since the bullet is fired horizontally, its initial vertical velocity is 0 m/s, and there is no vertical acceleration (in the absence of air resistance), so the equation simplifies to:
displacement = 0.5 x acceleration x time^2
The acceleration due to gravity is approximately 9.8 m/s^2.
displacement = 0.5 x (9.8 m/s^2) x (1/15 s)^2
displacement = approximately 0.0044 m
Therefore, the bullet will have dropped approximately 0.0044m in traveling a distance of 20m.
b) How far will the bullet have dropped in one second?
To find the vertical displacement in one second, we again need to use the equation of motion for vertical motion.
Step 1: Identify the time.
In this case, the time is given as 1 second.
Step 2: Calculate the vertical displacement using the equation of motion.
Using the same equation as before:
displacement = 0.5 x acceleration x time^2
displacement = 0.5 x (9.8 m/s^2) x (1 s)^2
displacement = 4.9 m
Therefore, the bullet will have dropped approximately 4.9m in one second.