Ahorizontal rifle is fired at a bull's-eye. the muzzle speed of the bullet is 700 m/s. the gun is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.023 m below the center. what is the horizontal distance between the end of the rifle and the bull's-eye?

The horizontal distance between the end of the rifle and the bull´s-eye is 48.3 m

Explanation:

Please, see the attached figure for a description of the problem.

Notice that the vector r, that describes the position of the bullet when it reaches the target, is composed of rx and ry (see figure). Then:

r = (rx, ry)

We know that ry is -0.023 m (the reference system is located at the end of the rifle), then:

r =(rx, -0.023 m)

The equation for the vertical position of the bullet at time t is as follows:

y = y0 +v0y · t + 1/2 · g · t²

Since the reference system is located at the end of the rifle, y0 = 0. The vertical component of the speed at t = 0 is 0, then, v0y = 0.

Then, we can calculate the time at which the vertical position of the bullet is -0.023 m:

-0.023 m = 0m + 0m/s ·t -1/2 · 9.8 m/s² · t²

-0.023 m/ -4.9 m/s² = t²

t = 0.069 s

The equation for the horizontal position is given by this expression:

x = x0 + v0x · t

Since the origin of the reference system is located where the bullet starts its trajectory, x0 = 0. To know the horizontal distance between the bull´s-eye and the end of the rifle, we have to find the horizontal position of the bullet at the time at which its vertical position is -0.023 m (0.069 s)

Then:

x = v0x · t

x = 700 m/s · 0.069 s = 48.3m

i don't understand. explain it clearly

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.