A hot-air balloon is rising vertically. the angle of elevation from a point on level ground 123 feet from the balloon to a point directly under the passenger compartment changes from 19.6 degrees to 29.4 degrees. how far, to the nearest tenth of a foot, does the balloon rise during this period?

25.5 feet

Explanation:

we are given the following:

initial angle of elevation = 19.6 degrees

final angle of elevation = 29.4 degrees

distance from the point of elevation = 123 feet

find the increase in height (rise) of the balloon ?

we should first take not that the hot air balloon,  the point of elevation on the ground and the point directly under the passenger form a right angel triangle with:

This heights can be gotten from applying the phytaghoras theorem where

tan (angle of elevation) =\frac{height}{adjacent side}

height = adjacent side × tan (angle if elevation)

(adjacent side is the distance from the point of elevation = 123 feet while the angle of elevation = 19.6 degrees and 29.4 degrees )

             height = 123 x tan 29.4 = 69.3 feet

             height = 123 x tan 19.6 = 43.8 feet

increase in height =69.3 - 43.8 = 25.5 feet

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j