a particle of unit mass is projected with velocity u at an inclination α above the horizon in a medium whose resistance is k times the velocity. its direction will again make the angle α with the horizon after a time......?
71Well, The resistance is determined by the magnitude of the initial velocity only or the variable velocity along the motion of the body?
11after time t say it acqiures velocity v then
resistive force is assumed in x direction only.
v=ucosα-kvt
from here we get
v(1+kt)=ucosα
v=ucosα/1+kt
also f=-kv
dv/dt=-kv
∫dv/v=-∫kdt
put value of limits in lhs as u to v(in terms of above) and on rhs 0 to t.
u get the answer.
1the resistance will b acting in both x and y directions and it depends on the velocity during the motion, not only the initial velocity.....
1@ JEE TOPPER
where did you use the condition that v is inclined at an angle α with the horizontal?
and what about the sine component of v?
1Vx = ucosα - kvt
Vy = usinα - gt
use tanα = Vy/Vx
and find out the value of v from these 3 equations.
Substitute them in the integral given by JEE TOPPER