Aman 2 m tall walks horizontally at a constant rate of 1 m/s toward the base of a tower 23 m tall. when the man is 10 m from the tower, at what rate is the angle of elevation changing if that angle is measured from the horizontal to the line joining the top of the man's head to the top of the tower? (round your answer to three decimal places.)

Explanation:

Given that

From the diagram

By differentiating with time t

When x= 10 m

θ = 64.53°

Now by putting the value in equation

Therefore rate of change in the angle is 0.038\ rad/s

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