Question

A balloon rises straight up at 10 ft/s. An observer is 40 ft away from the spot where the balloon left the ground. Find the rate of change (in radians per second) of the balloon’s angle of elevation when the balloon is 30 ft off the ground.

Answer 1

Please match the answer

Answer 2

the rate of change (in radians per second) of the balloon's angle of elevation = 25/64

Step-by-step explanation:

A balloon rises straight up at 10 ft/s.

=> dh/dt = 10

Tanα  = h/40

Differentiating wrt t

=> Sec²α dα/dt  = (1/40)dh/dt

=> Sec²α dα/dt  = (1/40)10

=> Sec²α dα/dt  = 1/4

=> dα/dt  = Sec²α/4

at height = 30 ft

tanα = 30/40 = 3/4

tan²α = 9/16

sec²α = 1 + tan²α = 1 + 9/16 = 25/16

=> dα/dt  =  (25/16)/4

=>  dα/dt  =  25/64

the rate of change (in radians per second) of the balloon's angle of elevation = 25/64

Learn more:

Find the rate of change of volume of a cone w.r.t. its radius, when the ...

https://brainly.in/question/5376336

A tree company charges a delivery fee for each tree purchased in ...

https://brainly.in/question/9824354