A man bailed out of a balloon After sometime the parachute opened up and he could land on the - Physics - Motion In A Straight Line

Question

A man bailed out of a balloon After sometime the parachute opened
up and he could land on the earth's surface at a retardation of 2 4
m s-2, and took 4 times the time that elapsed before the
parachute opened If the ballon was at a height of 398 4 m, how long
was the airborne? At what speed did he touch the ground?

Ujjval Chauhan · Accepted Answer

Dear student

The figure shows the situation
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57ea963997e58%20jpg"
style="width: 150px; height: 175px;">

At A when man bailed of the balloon he fall of under gravity so
from A to B: let at be the velocity of man is v then
v=u+gtv=0+gtv=9
8t                                            
(1)and398 4-y=0+12gt2398 4-y=9 82t2398 4-y=4
9t2                      
(2)
From B to C:
let the velocity of man when he touches the ground is v' then
v'=v+a·4tv'=9 8t-2 4×4tv'=9 8t-9 6tv'=0
2t                            
(3)and y=v·4t+12a4t2y=9 8t·4t-12×2
4×16t2y=39 2t2-19 2t2y=20t2but from (2)398 4-4
9t2=20t2t2=398 424 9t2=16⇒t=4 sec
Thus v'=0 2×4=0 8 m/s2 andy=20×16=320m