A pair of sunglasses fall from a hot air balloon, 225 m above the ground. If air resistance is negligible, calculate a) the time it takes for the sunglasses to reach the ground
b) the sunglasses' final velocity, right before they hit the ground

(a) The glasses are a height y above the ground at time t according to

y = 225 m - 1/2 g t²

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity. They reach the ground when y = 0 :

0 = 225 m - 1/2 g t²

t² = (450 m) / g

t ≈ 6.78 s

(b) The glasses have a velocity v of

v = - g t

so that at the time they hit the ground, they do so with a velocity of

v = - g (6.78 s)

v ≈ 66.4 m/s

overcharge is the right answer system