Question

7. A body of mass m-1kg initially is at position xo- -1m and starts moving away from the origin with speed to = 10m/sec. It is moving along the z axis under the influence of three forces (i) an attractive force towards the origin which is 8 times the position of the body (ii) the air resistance which is 6 times the velocity of the body; 160 (iii) and the kinetic friction with coefficient μ (a) The initial value problem for the position function of the body is Give a physical interpretation of each term in the above differential equation. 3 marks] (b) Derive the solution of the initial value problem in the previous part. It is given that the 2 9 marks] acceleration due to gravity is g - 9.8m/sec'. c)Find the time T>0 when the velocity of the body becomes instantly zero. Find the 4 marks] [4 marks] position of the body at time T d) Show that for t > T, the body is moving toward the origin.

Answer 1

0 kinetic dBUhon Noto r)

2 t Noto

c) VI4)- ут Lo -2T 0 Tn2 - 0.341« 2. χ(T): L.248-2.498-1 0.5 1 > 0.341. Vl)- 1o e-2xo.5 VID-3.679-2-101