Your instructor will walk at constant velocity beneath the announcer's booth of the varsity baseball field (a two-story tower). Your teammate will stand tall on top of the announcer booth's steps, with her or his dropping hand raised above his/her head. The egg must freefall to strike the helmet of the instructor.

What equation of motion would I use here? Just x=1/2at^2+vt?

d instructor = u t

find t so you can find d, how far the instructor is from directly under when you drop.

H = height
H = (1/2) g t^2
t = sqrt (2 H/g)

so d = u sqrt (2 H/g)

To solve this problem, we can start by analyzing the motion of the egg and the instructor. The egg is falling freely under gravity, while the instructor is walking with constant velocity.

Since the egg is in freefall, we can use the equation of motion for freefall:

y = y0 + v0t + (1/2)gt^2

Where:
- y is the final vertical position of the egg.
- y0 is the initial vertical position of the egg (above the helmet of the instructor).
- v0 is the initial vertical velocity of the egg (0 since it is dropped).
- g is the acceleration due to gravity (-9.8 m/s^2).
- t is the time taken for the egg to fall.

To find the time it takes for the egg to fall, we need to consider the height from which it is dropped. Let's assume the height is h.

y0 = h

Since the instructor is moving at a constant velocity, the horizontal position of the instructor (x) does not affect the vertical motion of the egg. Thus, we only need to focus on the vertical position (y).

Now, we need to consider the vertical position of the instructor's helmet. Let's assume the height of the helmet above the ground is H.

y = H

By setting y = y0 + v0t + (1/2)gt^2 equal to H, we can solve for the time it takes for the egg to fall and hit the helmet.

H = h + 0 + (1/2)(-9.8)t^2

Solving this equation will give you the time it takes for the egg to fall and strike the helmet of the instructor. Once you have the time, you can plug it back into the equation of motion to find the final vertical position of the egg if needed.