a) t is the time elapsed since the egg was dropped
b) h(t) is the height at some time, t
c) When it hits the ground, h(t) = 0
So....we can solve this
-16t^2 + 50 = 0
-16t^2 = -50 divide both sides by -2
8t^2 = 25 divide both sides by 8
t^2 = 25/8 take the square root
t = √[25/8] ≈ 1.77 sec
(d) At 1 sec the height is -16(1)^2 + 50 = 34 ft
At 1.5 sec the height is -16(1.5)^2 + 50 = 14 ft
So....it falls 34 -14 = 20 feet in this time interval