A gun shoots bullets that leave the muzzle with a speed of 341 m/s. If a bullet is to hit a target 171 m away at the level of the muzzle, the gun must be aimed at a point above the target. How far above the target is this point?
The time it takes to reach the target is 171/341 = 0.502 s
Calculate how far the bullet falls in that time. That is how high you should aim, above the target.
To determine how far above the target the gun must be aimed, we need to consider the effects of gravity on the bullet's trajectory.
First, let's assume that the bullet follows a parabolic path due to the combination of its initial forward velocity (341 m/s) and the force of gravity pulling it downwards.
We can break down the problem into two components:
1. The horizontal component: This is simply the distance traveled horizontally, which is given as 171 m.
2. The vertical component: This is the distance the bullet drops due to the force of gravity. We need to calculate this distance.
To find the time of flight, we'll use the formula:
Time = Distance / Velocity
Using the values given, we can calculate the time of flight for the bullet:
Time = 171 m / 341 m/s = 0.5 seconds
Since the bullet takes 0.5 seconds to reach the target horizontally, it will also take 0.5 seconds to fall vertically due to gravity.
The formula to calculate vertical displacement is:
Vertical Displacement = (0.5 * g * t^2)
Where:
g = acceleration due to gravity = 9.8 m/s^2
t = time of flight = 0.5 seconds
Therefore, the vertical displacement can be calculated as:
Vertical Displacement = (0.5 * 9.8 * 0.5^2) = 1.225 meters
Thus, the gun must be aimed approximately 1.225 meters (or 1.23 meters when rounded to two decimal places) above the target to compensate for the effect of gravity.