A ball is dropped from a ballon going up at a speed of 7m/s . If the ballon was at 60m at time of dropping the ball how long the ball take to reach ground level

Question

A ball is dropped from a ballon going up at a speed of 7m/s . If the ballon was at 60m at time of dropping the ball how long the ball takes to reach ground level .

Answer 1

Hello Tony,

 

First, let's take stock of our given info:

 

Δx=-60m   (negative because it moves down)

v₀=7m/s    (positive because it is up)

a=-9.81m/s²      (negative because it accelerates down.I assume this is the you are using for gravity.  If you are rounding differently, use that value instead.)

t=?

 

We want to choose a formula that only has  only one unknown value so we can solve for it.  Let's use:

Δx=v₀t+1/2at²

And plug in our values.

-60=7t+1/2(-9.81)t²

-60=7t-4.905t²

 

This looks like a quadratic, so lets set equal to 0

-4.905t² +7t+60=0

 

Now we can solve using the quadratic formula:

t=(-b±√(b²-4ac))/2a

a=-4.905

b=7

c=60

 

Plug in the values:

t=(-7±√(7²-4(-4.905)(60)))/(2*-4.905)

 =(-7±35.017)/14

t = -3.00s or t=2.00s

 

We have to throw out the negative answer since it doesn't make sense in asking how long it took for the ball to fall.  So our answer is 3 s.