A balloon, rising vertically with a velocity of 16 feet per second, releases a s

protisvitfc

protisvitfc

Answered question

2021-11-21

A sandbag is released by a balloon that is rising vertically at a speed of 16 feet per second when it reaches a height of 64 feet. (a) How long will it take the bag to hit the ground after it is released? (b) How quickly will it strike the ground?

Answer & Explanation

Fachur

Fachur

Beginner2021-11-22Added 17 answers

a)
We will use the formula:
s=ut+12at2
The bag will hit the ground when x=-64
Substitute: u=+16, because initial velocity of bag after release is 16ft/s
Substitute: a=-32
64=16t+12(32)t2
16t216t64=0
Divide throughout by 16
t2t4=0
Using the quadratic formula
t=(1)±(1)24(1)(4)2(1)
t=1±1+162
t=1±172
t must be positive, so we reject the negative solution
t=1+1722.562
The bag will hit the ground after 2.562 seconds
b) v=u+at
Substitute: u=16, a=-32 and t=2.562
v=16+(32)(2.562)=65.984
The bag will hit the ground with a speed of 65.984 ft/sec

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