A shell is fired from a gun with a muzzle velocity of 466 m/s, at an angle of 57.4° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming level terrain?

Sure, let's break this down step by step. Firstly, we have a shell fired from a gun with a muzzle velocity of 466 m/s at an angle of 57.4° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment falls vertically with a speed of zero immediately after the explosion.

Finding the Time of Flight

To find how far the other fragment lands, we need to calculate the time of flight for the shell before it explodes. We can do this by using the vertical component of the initial velocity (u) and acceleration due to gravity (g).

Given: u = 466 m/s, θ = 57.4°

Vertical component of initial velocity (u_y) = u * sin(θ)

Time of flight (t) = 2 * (u_y / g)

Calculating the Horizontal Distance

Now that we have the time of flight, we can determine the horizontal distance the other fragment lands from the gun. This can be calculated using the horizontal component of the initial velocity (u_x) and the time of flight (t).

Horizontal component of initial velocity (u_x) = u * cos(θ)

Horizontal distance = u_x * t

Putting It All Together

By plugging in the values, calculating the time of flight and the horizontal distance, we can find out how far the other fragment lands from the gun.

Remember to consider the effects of air resistance, which might slightly alter the actual landing distance in a real-world scenario.

So, by using the principles of projectile motion and analyzing the given parameters, we can determine the horizontal distance at which the other fragment lands from the gun after the shell explodes.