a bullet is fire in a horizontal direction with a
muzzle velocity of 300m/s in the absence of air
resistance, how far will it have dropped in travely
a horizontal distance of(a)20m?(b)40m?(c)60m?
how far will it drop in one second
To find out how far a bullet will drop in a horizontal distance, we need to consider the time it takes for the bullet to travel that distance. We can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, since the bullet is fired horizontally with no air resistance, the vertical acceleration is due to gravity (g = 9.8 m/s^2), and the initial vertical velocity is 0 (since it's fired horizontally). Therefore, the equation simplifies to:
distance = (1/2) * g * time^2
Now let's calculate the distances for each part of the question:
(a) For a horizontal distance of 20m:
We want to find the time it takes for the bullet to travel that distance. Rearranging the equation, we have:
time = sqrt((2 * distance) / g)
time = sqrt((2 * 20) / 9.8)
time = sqrt(4.08)
time ≈ 2.02 seconds
Now we can calculate the vertical distance dropped:
distance = (1/2) * g * time^2
distance = (1/2) * 9.8 * (2.02)^2
distance ≈ 19.9 meters
Therefore, the bullet will have dropped approximately 19.9 meters when traveling a horizontal distance of 20 meters.
(b) For a horizontal distance of 40m:
Using the same formula, we have:
time = sqrt((2 * 40) / 9.8)
time ≈ 2.86 seconds
distance = (1/2) * 9.8 * (2.86)^2
distance ≈ 49.5 meters
So, the bullet will have dropped approximately 49.5 meters when traveling a horizontal distance of 40 meters.
(c) For a horizontal distance of 60m:
Again, using the same formula:
time = sqrt((2 * 60) / 9.8)
time ≈ 3.47 seconds
distance = (1/2) * 9.8 * (3.47)^2
distance ≈ 107.8 meters
Thus, the bullet will have dropped approximately 107.8 meters when traveling a horizontal distance of 60 meters.
To calculate how far the bullet will drop in one second:
Since we already know the time it takes for the bullet to travel a horizontal distance, we can directly substitute that value into the distance equation:
distance = (1/2) * 9.8 * (time)^2
For example, if we consider the bullet's initial horizontal velocity of 300 m/s, the time it takes for the bullet to travel one second horizontally would be 1 second. So we can substitute that value into the equation:
distance = (1/2) * 9.8 * (1)^2
distance ≈ 4.9 meters
Therefore, the bullet will drop approximately 4.9 meters in one second.
how long did it take to get 20 m?
time=distance/velocity=20/300 sec
how far did it drop?
distance=1/2 g time^2