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

when a device is used in a circuit in which the voltage is 81 v, the current flowing through the device is 3 a. what is the resistance of the device?

a. 27 ω

b. 40.5 a

c. 243 ω

d. 243 a

the correct answer is a. 27

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day