How Fast is a Balloon Rising if a Dropped Coin Hits the Ground in 4 Seconds?

[fraserperry]

Hard Motion Question- Help?

I am really stuck on this motion question, can anyone help please?

"A balloon is 30.00m above the ground and is rising vertically with a uniform speed when a coin is dropped from it. If the coin reaches the ground in 4.00 seconds, what is the speed of the balloon?

 

[Ben Niehoff]

So, the coin has an initial height of 30 m, and an initial velocity of v. It has a constant acceleration of -9.8 m/s^2. Find the time it takes to fall to a height of 0 m, in terms of your variables v and t. Then plug in 4.00 s for t, and solve for v.

 

[fraserperry]

which motion equation do i use?

 

[rsala]

solve for the initial velocity of the coin,,since it is equal to the constant velocity of the balloon, try

0 = 30 + Vi * 4 - .5g(4^2)

thing to know is that if the balloon is traveling , say 500 m/s when the coin is dropped...the coin is actually dropped AT 500m's...so its initial velocity when you insert it into an equation is 500m/s,, NOT 0 as you might assume.
though that's irrelevant here, thought i might say. so that you understand the purpose of the question really

 

[fraserperry]

are you saying the coin when dropped is would be traveling the same speed of the balloon in an upwards direction?

 

[rsala]

yes, you and its acceleration is changed from 0 to -9.8 when you put it in the equation because of gravity...because of course it will be hitting the ground soon

 

[fraserperry]

I got 12.1 from that equation, but what is that number?

 

[rsala]

the coins initial velocity once it is released from the balloon. = 12.1

which just so happens to be the balloons constant velocity, since when you initially dropped the coin from the balloon its initial velocity is = to the balloon velocity.
so, Balloon-velocity = 12.1

ithink