12. A balloon is rising with a constant speed of 5 m/s. It carries a basket with
ID: 1660198 • Letter: 1
Question
12. A balloon is rising with a constant speed of 5 m/s. It carries a basket with a person inside. When the balloon is a 120 m above the ground the person holds an object outside the basket and lets it go. a) Describe the motion of the object as seen by a person on the ground and as seen by the person in the balloon's basket. What maximum height does the object rise above the ground? c) How long does it take the object to reach its maximum height? ...to hit the ground? d) How fast is it going when it hits the ground? e) If the person had thrown the object downward with a speed of 10 m/s relative to the balloon (instead of merely letting go), how long would the object take to hit the ground in that case?Explanation / Answer
a)velocity of gallon(u)=5m/s
Height (h)=120m
The person on the ground feels that as if the stone is projected upwards with a velocity of 5m/s from a height of 120 m from ground
b)H=maximum height reached by stone above the ground
=h+(u^2/2g)
=120+(5^2/(2*9.8))
=121.27m
c)time taken to reach maximum height is (t1)= u/g=5/9.8sec=0.51 sec
t2=time taken by stone to reach ground from maximum height=sqrt(2H/g)=((2*121.27)/9.8)=4.97 sec
Total time to reach ground is =t1+t2=0.51+4.97=5.48sec
d)v=speed of stone it hits the ground=g*t2=9.8*4.97=48.8m/s
e)v1=speed of stone relative to ballon=10m/sdown ward
Velocity of stone relative to ground (v2)=v1+u=10+5=15m/s
Time taken to reach ground is=t3=?
S=ut+(1/2)at^2
120=15t+(1/2)*9.8t^2
4.9t^2+15t-120=0 on solving this equation we get
T=3.65sec
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.