Question

A hot air balloon is traveling vertically upward at a constant speed of 2.8 m/s. When
it is 29 m above the ground, a package is
released from the balloon.
After it is released, for how long is the
package in the air? The acceleration of gravity
is 9.8 m/s^2.
Answer in units of s


What is its speed just before impact with the
ground?
Answer in units of m/s

I have the setup:
0=29 m+2.8m/s(t)+.5(-9.8m/s)(t^2)

Formula: x= x(initial) + v(initial)(t) +.5a(t^2)

Answer 1

why is your formula x=? if i'm reading it right the formula is the height of the object at time t.

That being the case, set your setup (which looks right) equal to 0 and solve for t.

This will tell you how long it takes to hit the ground.

Plug this value of t into the forumla -9.8t+2.8 and that will tell you the speed at time t.

Answer 2

Oh..i see...your formula is using x instead of s (which is what i'm used to).

Nevermind...the rest of my post will help though.

Answer 3

x(final)=x(initial)+v(initial)t+a(t^2)
where x is vertical distance. looks right

Answer 4

i know what the setup is, i just don't know what steps to take to solve for t

Answer 5

So recap...solve\[-0.49t^{2}+2.8t+29=0\]for t

Answer 6

quadratic equation

Answer 7

then plug this into the formula -9.8t+2.8 and it will tell you the instantaneous speed at time t (which is just as it hits the ground)

Answer 8

thanks

Answer 9

np

Answer 10

initial velocity of package = -2.8m/sec
package has to travel distance= 29 m
time it float in air is
s =ut +1/2 a t^2
29= -2.8 * t + 0.5 * 9.8 * t^2
solve this equation you will get time..(ignore negative value of time)

speed at ground(when it hit) is
v =u + a* t
=-2.8 + 9.8* t (put your t ;which you got from above quadratic equation)

this is the elegant solution of this problem.

Answer 11

That's actually the same solution method I gave :)

Answer 12

Only difference is whether your final answer is positive or negative...the correctness of each is a matter of debate.

Answer 13

there is a another but lenthy way of solving this problem is first move package up and see how much time it will take to get velocity zero..then make it fall down...calculate everything for both cases...and then add.