Question

3) A person wants to drop a package from an airplane to the people below. If the plane is flying horizontally at 120 km/hr and drops the package from 60 m above the flat surface. (Neglect air resistance for parts a) and a) If the person in the airplane wants to have the package land 20m behind the people on the ground, where should the person drop the package. (Clearly define a coordinate system so we understand your answer) b) What is the largest time error the person can make while dropping the package to ensure the people on the ground are not hit by the package? c) If we do not neglect air resistance, describe qualitatively what would change about your two previous answers.

Answer 1

of the airplane where AB is the height of package landing when people are just at the bottom of the airplane and BC is the distance behind the 60m people. So we have to В 20m find AC

(a) In triangle ABC, by pythagoras theorem,

(AC)² = (AB)² + (BC)²

(AC)² = (60)² + (20)² = 3600 + 400 = 4000

(AC)² = 4000

taking underoot both sides, we get,

AC = 63.245 m , which the distance of the plane from the ground so that the man in the plane will drop the package 20m behind the people.

(b) Since the distance is 60m from the ground, therefore, the initial velocity of the box will be zero, therefore, by applying newton's second equation we will find the time in which the box will hit the ground, therefore,

H = ut + 1/2 at² since u = 0 , then

60 = 0 + 1/2 x 9.8 x t²

120 = 9.8 x t² ,

120/ 9.8 = t²

t = 12.24 sec

therefore, the largest time error will be = 12.24% .

(c) If the air resistance is taken into consideration, therefore, we also have to find the air drag in the above two situations which will affect the values obtained in the above cases.