To calculate the speed of the projectile at the end of the coilgun, we need to use kinematic equations.

First, we need to determine the acceleration of the projectile. We know that the coilgun accelerates the projectile using a magnetic field, but we don't have any information about the force or time. Therefore, we need to find the acceleration using the kinematic equation:

v^2 = u^2 + 2as

Here, v is the final velocity of the projectile at the end of the coilgun, u is the initial velocity (which is zero as the projectile starts at rest), a is acceleration, and s is the distance traveled (2 meters).

Since the projectile starts from rest, its initial velocity is 0 m/s. Plugging in the values:

v^2 = 0^2 + 2a(2)

Simplifying:

v^2 = 4a

Next, we can find the acceleration by using the formula:

F = ma

Here, F is the force, m is the mass of the projectile (0.1 kg), and a is the acceleration.

However, we are not given the force acting on the projectile. So, let's assume a typical coilgun can produce a force of 1000 Newtons. Plugging the values into the formula:

1000 N = 0.1 kg * a

Simplifying:

a = 10000 N/kg

Now, let's substitute the value of acceleration into the first equation:

v^2 = 4 * 10000 N/kg * 2 m

v^2 = 80000 N*m/kg

Taking the square root:

v ≈ 282.8 m/s

Therefore, the speed of the projectile at the end of the coilgun is approximately 282.8 m/s.

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