7. A balloon is ascending at the rate of 9.8 m/s at a height of 39.2 m. above the ground, when a food packet is released from it. If it strikes with more than 30 m/s it will burst. So find will it burst or not.
Answers
Answer:
So when food is dropped it will have same velocity as balloon but gravity in opposite . So it will go to a height then stop and the start coming downwards.
We will use above as +ve and below as negative for vector purpose.
So initial velocity is 9.8 m/s . Acceleration is -9.8m/s^2
So by applying v²-u²=2as
0² -( 9.8)² = 2(-9.8)s
S=4.9m
It means food reached a top of 39.2+4.9m=44.1 m
By v=u+ at we can find out
0 =9.8+(-9.8)t that food reached on top in 1 second and came to zero velocity .
Now at 43.1 meter food velocity is zero and now it will be condition of free fall under gravity .
So we know u=0 , a=-9.8 , s =-44.1m v=?
Again v²-u²=2as
V²= 2(-9.8)(44.1)
V=29.4m/s
And by s =ut + 1/2at²
-44.1 =0+1/2(-9.8)t²
T²=9
T=3 seconds.
Because initial it required 1 second to come at a stop on its top thus total time is 1+3=4 sec.
So it will hit ground in 4sec with a velocity of 29.4m/s.
Another question total displacement covered by stone after dropping from balloon =39.2 m , total distance is 4.9+4.9+39.2m .as we calculated after ascending 4.9 meter it was on top.
IT CAN BE SOLVED BY EASIER METHOD .But usually these types of questions have multiple questions in it so by this way you can answer them all .
Easier methods requires extra care on vectors and directions (+&-signs).
So we will take up as +ve and down as -ve
So s=-39.2m (it's displacement not distance)(negative because it will come down)
a= -9.8 as it is acting downwards.
U= 9.8 m/s as balloon was going upwards.
Thus v²-u²=2as
V²-9.8² = 2 (-9.8)(-39.2)
V²=864.36
V=29.4m/s (it is in positive because we didn't take v as negative ; -v)
And by s=ut+1/2at²
-39.2=9.8t+1/2(-9.8)t²
-4=t-0.5t² (divided by 9.8)
-8=2t-t²
T²-2t-8=0
By solving it t=4 seconds.