A rifle with muzzle velocity of 460m\s shoot a bullet at small target 46 metre away. How high above the target must the gun be aimed so that the bullet will hit the target.
assuming the target is horizontal from the gun.
distance bullet falls:
h=1/2 g t^2 where the time is from
t=46/460 seconds
h=1/2 (9.8)(46/460)^2
To determine the height above the target the gun should be aimed, we need to consider the horizontal and vertical components of the bullet's motion.
First, let's find the time it takes for the bullet to travel horizontally to the target. We can use the formula:
Time = Distance / Velocity
Time = 46 m / 460 m/s
Time = 0.1 seconds
Now, let's consider the vertical motion of the bullet. Assuming no air resistance, the bullet will follow a parabolic trajectory due to the effect of gravity. The key point to note here is that the time it takes for the bullet to reach its peak height is equal to half the total flight time.
Using this information, we can calculate the bullet's total time of flight:
Total Time = 2 * Time to reach peak height
Total Time = 2 * 0.1 seconds
Total Time = 0.2 seconds
Now, let's find the vertical displacement of the bullet during this time. We can use the kinematic equation:
Vertical Displacement = Initial Vertical Velocity * Time + (0.5 * Acceleration * Time^2)
Since the bullet is initially fired horizontally, its initial vertical velocity is zero. The acceleration due to gravity is approximately 9.8 m/s^2.
Vertical Displacement = 0 * 0.2 + (0.5 * 9.8 * 0.2^2)
Vertical Displacement = 0.196 m
Therefore, the gun should be aimed approximately 0.196 meters (or 19.6 centimeters) above the target so that the bullet will hit it.