Question : A small parachute, dropped from a 30m high cliff, falls freely under gravity for 1 second and then attains a terminal velocity of 1.2 m/s. If a stone is dropped from the cliff 20 seconds after the parachute was dropped, will the stone catch up with the parachute before it reaches the ground?
Doubt by Ishmeet
Solution :
Total Distance Covered by Parachute (h)
=30 m
Terminal Velocity (Constant Velocity) of Parachute = 1.2 m/s
=30 m
Terminal Velocity (Constant Velocity) of Parachute = 1.2 m/s
Distance Covered by the Parachute during Free Fall which happens for t1=1 Second
Using
s=ut+½gt²
s=ut1+½gt1²
s=(0)(1)+½(9.8)(1)²
s=4.9 m
Using
s=ut+½gt²
s=ut1+½gt1²
s=(0)(1)+½(9.8)(1)²
s=4.9 m
Distance Covered by the Parachute with Terminal (Constant) velocity of 1.2 m/s
= 30-4.9
=25.1 m
= 30-4.9
=25.1 m
Time Taken by the parachute to cover this distance with constant velocity
s=ut+½at²
s'=ut2+½(0)t2²
25.1=(1.2)t2+0
25.1/1.2=t2
20.916=t2
t2=20.92 sec
s=ut+½at²
s'=ut2+½(0)t2²
25.1=(1.2)t2+0
25.1/1.2=t2
20.916=t2
t2=20.92 sec
Total Time taken by the parachute to come down
= t1+t2
= 1+20.92
= 21.92 sec
= t1+t2
= 1+20.92
= 21.92 sec
Now, the stone is thrown after 20 sec the parachute is released
Time Taken by the stone to come to the ground
Using
Time Taken by the stone to come to the ground
Using
s=ut+½at²
h=(0)t+½gt²
30=0+½(9.8)t²
30=4.9t²
30/4.9=t²
t²=6.122
t²=6.12
t=√6.12
t=2.473
t=2.473 sec
Total Time taken by the stone to come down to the earth
=20 + 2.473
=22.473
=22.47 sec
h=(0)t+½gt²
30=0+½(9.8)t²
30=4.9t²
30/4.9=t²
t²=6.122
t²=6.12
t=√6.12
t=2.473
t=2.473 sec
Total Time taken by the stone to come down to the earth
=20 + 2.473
=22.473
=22.47 sec
This time is less than the time taken by the parachute (21.92 sec). So, the parachute hit the ground first and then the stone will reach the ground.
No, the stone will not catch the parachute before it reaches the ground.