Question

a body of mass m is thrown into air. it takes a parabolic path. consider three points a,b and c along its path in air, in that order. their position vectors are given by ra, rb and rc respectively. work done on the body by the gravitational force during the journey from a to c is given by

Answer 1

Explanation:

A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any games. Find the ratio of number of members who play

Answer 2

Given:

A body of mass m undergoing a projectile motion

ra, rb and rc are position vectors of points A, B, and C respectively

To find:

Work done on the body by the gravitational force during the journey from a to c.

Solution:

We know that work done by gravity on an object with mass m and at height h is given by mgh.

Position vectors ra, rb, and rc are the shortest distance between the origin and points A, B, and C respectively. (Refer to the diagram attached below).

If ∅ is the angle of projection from the initial point O, then the vertical height of the body at points A, B, and C are:

ra sin α1 , rb sinα2, and rc sinα3 respectively.

Hence, the work done on the body by the gravitational force at

Point A = m.g.ra sin α1

Point B = m.g.rb sin α2

Point C = m.g.rc sin α3