An airplane is flying in still air with an airspeed of 275 mi/hr. If it is climb

Question

An airplane is flying in still air with an airspeed of 275 mi/hr. If it is climbing at an angle of 18 degrees, find the rate at which it is gaining altitude.

Explanation / Answer

speed of airplane,| v | = 275 mi/hr ..................................................................................................................................................... here ' v ' is the velocity and | v | is the magnitude i.e. speed .. ..................................................................................................................................................... v = vx i + vy j , vx = velocity in horizontal direction , vy = velocity in vertical direction ..................................................................................................................................................... tan(angle) = vy / vx , here angle = 18 degrees , ..................................................................................................................................................... vx = vy / tan(angle) = vy / tan(18) = vy / 0.325 = 3.08*vy ..................................................................................................................................................... since, | v | = root [ (vx)^2 + (vy)^2 ] = 275 ..................................................................................................................................................... =>root [ [(3.08)^2+1]*(vy)^2 ] = 275 ..................................................................................................................................................... => vy * root [(3.08)^2+1] = 275 ..................................................................................................................................................... => vy * 3.24 = 275 ..................................................................................................................................................... => vy = 84.88 mi/hr , i.e. , 85 mi/hr ...........Answer.....

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