Ahot air balloon is flying above grovenburg. to the left side of the balloon, the balloonist measure the angle of depression to the groveburg soccer fields to be 20 degrees 15’. to the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62 degrees 30’. the distance between the two athletic complexes is 4 miles.

Angle x = 90° - 22°15’  

Angle y = 90° - 62°30'

Angle z = 22°15’ = 22.25°

Angle w = 62°30’ = 62.50°

tan(z) = H/a => a = H/tan(z)

tan(w) = H/b => b = H/tan(w)

a+b = 4 => H/tan(z) + H/tan(w) = 4 => H [1/tan(z) + 1/tan(x) ] = 4

    H = 4 / {[1/tan(z) + 1/tan(x) ] } = 1.35 miles

    a = 1.35 / tan(22.25°) =  3.30 miles

    b = 4 – 3.30 = 0.7 miles

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r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min