I need help with this physics problem and drawingits visual representation: You
ID: 3278890 • Letter: I
Question
I need help with this physics problem and drawingits visual representation: You have an internship with the Exploratorium, in San Francisco, and your supervisor (a chemist) has a great new idea for a demo. Two small balloons will be filled with different chemicals that create a big burst of light when they react. One will be dropped from the ceiling and another will be shot up from the floor, released at the same moment. The reaction will happen best if the balloon heading upwards is traveling at the same speed as the balloon heading downwards, when they collide. One engineer is building the rig to drop the balloon, but doesn’t know the exact height it will be dropped from yet. Another is building the balloon launcher, which will have an adjustable launch speed. Your supervisor is worried about the height that the collision will occur at, and wants to make sure it is above everyone’s head. What can you say?
(You need to draw a visual representation for the problem before solving it. The 'form' may be a plot, motion diagram, sketch, or free body diagram(s). You may use more than one. The representation needs to be complete and clear, presenting all of the variables used in the problem.You also need to specify the physics model that you are using to solve the preoblem)
Explanation / Answer
let the top baloon be dropped from height h, then after time t
its speed is v and it has travelled a distance y
so, y = 0.5gt^2
and v = gt
for the baloon launched from bottom, let initial speed be u ( this is controllable)
then after time t, speeed should be equal to the speed of dropping baloon for the reaction to occur best
so, v = u - gt
gt = u - gt
u = 2gt .. (1)
Also, distance travelled by this baloon should be h - y
h - y = ut - 0.5gt^2
h - y = 2gt^2 - 0.5gt^2 = 1.5gt^2
h = 1.5gt^2 + 0.5gt^2 = 2gt^2
now h - y > 2 m ( above everyone's head)
so, 1.5gt^2 > 2
t > 0.368 s
or h > 2.6667
also u = 2g*t
2gt^2 = h
so, u = 2g*sqroot(h/2g) = sqroot(2gh)
hence the height at which the top baloon is dropped should be greater than 2.667 m
and the velocity weith which the second baloon is fired up is sqroot(2*gh)