A bullet is fired in a horizontal direction with a muzzle velocity of 300ms-1. In the absence of air resistance, how far will it have dropped in travelling a horizontal distance of: a.20m b. 40m c. 60m d. How far will it drop in one second.
To determine how far a bullet will drop in a horizontal distance, we need to use the concepts of projectile motion. Here's how you can calculate the vertical displacement for each scenario:
a. 20m:
In the absence of air resistance, the bullet's horizontal velocity remains constant throughout its motion. Therefore, the time it takes to travel 20m horizontally can be calculated using the formula: time = distance / velocity. In this case, time = 20m / 300ms-1 = 0.0667 seconds.
Since the bullet is fired horizontally, its initial vertical velocity is 0ms-1 (no upward or downward movement initially). The gravitational acceleration, g, acts vertically downward, and its value is approximately 9.8ms-2.
Using the equation for vertical displacement (assuming no initial vertical velocity):
vertical displacement = 0.5 * g * time²
Plugging in the values, we get:
vertical displacement = 0.5 * 9.8ms-2 * (0.0667s)² ≈ 0.022m
Therefore, the bullet will drop approximately 0.022m when traveling a horizontal distance of 20m.
b. 40m:
Using the same method as above:
time = 40m / 300ms-1 = 0.1333 seconds
vertical displacement = 0.5 * 9.8ms-2 * (0.1333s)² ≈ 0.088m
Hence, the bullet will drop approximately 0.088m when traveling a distance of 40m.
c. 60m:
Again, using the same approach:
time = 60m / 300ms-1 = 0.2 seconds
vertical displacement = 0.5 * 9.8ms-2 * (0.2s)² ≈ 0.196m
The bullet will drop approximately 0.196m when traveling a distance of 60m.
d. To find how far the bullet will drop in one second, we can directly use the equation for vertical displacement and substitute the time as 1 second:
vertical displacement = 0.5 * 9.8ms-2 * (1s)² = 4.9m
Therefore, the bullet will drop approximately 4.9m in one second.
Keep in mind that these calculations are based on the assumption of no air resistance, which may not be entirely accurate in real-world scenarios.