Projectile Motion
A rifle is fired horizontally and travels 200m East. The rifle barrel is 1.90m from the ground. What speed must the bullet have been traveling at? Ignore Friction.
First, the motion in the x direction is as simple as x=v*t; so you know that your speed is x/t, or 200/t.
In the y direction you have acceleration, so you need x=v*t+a*t^2
the distance traveled in the y direction is 1.90m (you got x), the velocity is 200/t( you got v, the acceleration is gravity ( you got a), the only thing left is to solve for time, and after that come back to the initial equation v=x/t, and that's it
:)
To determine the speed at which the bullet must have been traveling, we can use the equations of projectile motion. Since the rifle is fired horizontally, the initial vertical velocity is 0 m/s.
We can use the equation:
d = v*t
where:
- d is distance traveled in the x-direction (in this case, 200m)
- v is the velocity of the bullet in the x-direction (horizontal velocity)
- t is the time of flight
Since the initial vertical velocity is 0 m/s, the time of flight can be determined using the equation:
t = sqrt(2h/g)
where:
- h is the height of the rifle barrel from the ground (1.90m)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values, we get:
t = sqrt(2*1.9 / 9.8)
t ≈ sqrt(0.3878)
t ≈ 0.6222 seconds (rounded to four decimal places)
Now, we can solve for the velocity (v) using the equation:
v = d / t
Plugging in the values, we get:
v = 200 / 0.6222
v ≈ 321.2556 m/s (rounded to four decimal places)
Therefore, the speed at which the bullet must have been traveling is approximately 321.2556 m/s.
To find the speed at which the bullet must have been traveling, we can use the concept of projectile motion.
In projectile motion, an object is launched at an angle or vertically and moves along a curved path under the influence of gravity. In this case, since the rifle is fired horizontally, the bullet is launched at an angle of 0 degrees with respect to the ground.
The horizontal component of the bullet's velocity remains constant throughout its motion, as there is no acceleration acting horizontally. Therefore, the horizontal distance traveled by the bullet is equal to its horizontal velocity multiplied by the time of flight.
In this problem, the bullet travels in the East direction, i.e., along the positive x-axis. The horizontal distance traveled is given as 200m. So, we can set up the equation:
Horizontal distance = Horizontal velocity × Time
200m = (Horizontal velocity) × (Time)
The vertical motion of the bullet is influenced by gravity. In the absence of any initial vertical velocity, the bullet will undergo free fall and follow a parabolic trajectory. The vertical displacement of the bullet is the distance from the rifle barrel to the ground, given as 1.9m.
The time taken for an object to fall freely from a height can be determined using the equation:
Vertical displacement = 0.5 × acceleration due to gravity × (Time)^2
1.9m = 0.5 × 9.8 m/s^2 × (Time)^2
Simplifying, we get:
(Time)^2 = (1.9m × 2) / 9.8 m/s^2
Time = √((1.9m × 2) / 9.8 m/s^2)
Now that we know the time of flight, we can substitute this value back into the equation for the horizontal distance to solve for the horizontal velocity:
200m = (Horizontal velocity) × (√((1.9m × 2) / 9.8 m/s^2))
Simplifying, we find:
Horizontal velocity = 200m / (√((1.9m × 2) / 9.8 m/s^2))
Evaluating this expression will give us the required speed at which the bullet must have been traveling.