Derivatives word problem

Question

Find the velocity of an air conditioner accidently dropped from a height of 300m at the moment it hits the ground

Answer 1

Assuming upward direction is positive, and neglecting air resistance,

 

h(t) = h₀ - (1/2)gt²

 

g = 9.8 m/s²

 

h₀ = 300 m

 

v(t) = dh/dt = -gt

 

When it reaches the ground,

 

h = 0 ⇒ 300 = (1/2)(9.8)t²

t = √(2*300/9.8) s = 7.82 s

 

v(7.82) = -9.8*7.82 m/s ≅ -76.6 m/s