Question

Alexandra drops an egg from 30 m above the ground to hit Vanessa on the head. If Vanessa stands 3.5 meters tall. How fast is the egg moving when it strike her head? (Hint: Draw a picture and you will see why you have to consider her height and find the time first!)

Answer 1

This is the problem. It's worth saying that I'm working with the magnitudes and their respective scalar equations. That is, I'm not using vectors.
v_e_g_g_,_i = 0m/s
g = 9.81m/s^2
h_i = 30m
h_f = 3.5m
v_e_g_g_,_f = ?
t = ?
|h_f-h_i| = v_e_g_g_,_i*t + (g*t^2)/2
26.5m = 0m/s*t + ((9.81m/s^2)*(t^2))/2
t = \sqrt{2*26.5m/(9.81m/s^2)} = 2.32 s
v_e_g_g_,_f = v_e_g_g_,_i + g*t
v_e_g_g_,_f = 0m/s+(9.81m/s^2)*(2.32 s)
v_e_g_g_,_f = 22.76 m/s