A shell is shot with an inital velocity of 20m/s at an angle 60 degrees with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment whose speed is immediately after the explosion zero falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and the air drag is negligible?

Would I use v^2 =v_o^2 +2ad? and solve for d? but would I also use F=ma to find a?

To find the distance from the gun where the other fragment lands, you can use the projectile motion equations. The equation you mentioned, v^2 = v_o^2 + 2ad, is a valid equation to use for the horizontal direction of motion.

Here's how you can approach the problem:

1. Resolve the initial velocity into horizontal and vertical components:

The initial velocity (v_o) is 20 m/s at an angle of 60 degrees with the horizontal. The horizontal component (v_o_x) can be found by multiplying the initial velocity by the cosine of the angle, and the vertical component (v_o_y) can be found by multiplying the initial velocity by the sine of the angle.

v_o_x = v_o * cos(60)
v_o_y = v_o * sin(60)

2. Determine the time of flight:

The time it takes for the shell to reach the highest point of its trajectory is the same as the time it takes for the vertically falling fragment to fall back to the ground. You can use the equation v = u + at to find the time of flight for the vertical motion. In this case, the initial velocity (u) is zero, and the acceleration (a) is gravity (-9.8 m/s^2).

v = u + at
0 = 0 + (-9.8) * t

Solving for t, you get:
t = 0 seconds (since the initial vertical velocity is zero)

3. Calculate the horizontal distance traveled:

Knowing the time of flight, you can now use the horizontal motion equation d = v_o_x * t to find the horizontal distance traveled.

d = v_o_x * t

4. Substitute the values:

Plug in the values calculated in step 1 and step 3 into the equation to find the distance from the gun where the other fragment lands.

d = v_o_x * t

5. Solve for the horizontal distance:

Calculate the horizontal distance traveled by substituting the values calculated above.

d = v_o_x * t

Since t is zero (as found in step 2), the horizontal distance traveled will also be zero. This means that the other fragment falls vertically at the same point where the shell exploded.

So, the final answer is that the other fragment lands at the same spot from the gun where the shell exploded.