science
posted by Pratapveer .
Mary wants to throw a can straight up into the air and then hit it with a second can. She wants the collision to occur at height h=5.0 m above the throw point. In addition, she knows that she needs t1=4.0 s between successive throws. Assuming that she throws both cans with the same speed. Take g to be 9.81 m/s2.
(a) How long it takes (in s) after the first can has been thrown into the air for the two cans to collide?
Δt=

h first one: Vi*t4.9t^2
h second one: Vi(t4)4.9(t4)^2
because the heights are the same, set the equations equal, solve for t. 
If both cans are thrown with the same velocity, then the first can must be on its way down when they collide, and the first can will be going up.
For the first can,
vt4.9t^2 = 5
t = 5/49 (v+√(v^298))
the 2nd can has been going up for only t4 seconds, so
v(5/49 (v+√(v^298))4)4.9((5/49 (v+√(v^298)))4)^2 = 5
v = 21.958 m/s ... call it 22m/s
Check:
22t4.9t^2 = 5 at t=4.25s and at t=0.25s
So, the 2nd can meets the 1st on its way down in 0.25 seconds. 
Let the initial velocity be v.
At some time Δt the displacement of both cans is the same (h), so by using the the equations for displacement under constant acceleration, we obtain two simultaneous equations:
For the first can:
h = v Δt  g (Δt)^2 /2
For the second can (launched at t1):
h = v (Δtt1)  g (Δtt1)^2 /2
We need to find Δt
Rearrange the first equation:
v = h/Δt + gΔt/2
Substitute this into the second equation.
h = (h/Δt + gΔt/2)*(Δtt1)  g*(Δtt1)^2/2
This will simplify into a quadratic equation which can be solved for Δt.
...
Once you have t then use (from above):
v = h/t + gt/2
Respond to this Question
Similar Questions

Physics
Suppose you throw a stone straight up with an initial speed of 15.00 m/s If you throw a second stone straight up 1.00s after the first, with what speed must you throw the second stone if it is to hit the first at a height of 11.0? 
math
You are standing on a bridge over a creek, holding a stone 20 feet above the water. 1. You release the stone. How long will it take the stone to hit the water? 
physics
A suspension bridge is 66.0 m above the level base of a gorge. A stone is thrown or dropped from the bridge. At the location of the bridge, g has been measured to be 9.83 m/s2. In each of the following, assume that there is no air … 
science (physics) IV
anton plan that he can throw at a dart board from a distance of 2 meters and hit the 5 centimeters wide bull's eye if he throw the dart horizontally with a speed of 20 meters per second. he start the throw at the height as the top … 
Phyiscs
Suppose you throw a stone straight up with an initial velocity of 27.0 m/s and, 5.5 s later you throw a second stone straight up with the same initial velocity. The first stone going down will meet the second stone going up. At what … 
mitx 8.01x Classical Mechanics
Mary wants to throw a can straight up into the air and then hit it with a second can. She wants the collision to occur at height h=5.0 m above the throw point. In addition, s/he knows that she needs t1=3.0 s between successive throws. … 
MITx: 8.01x Classical Mechanics
Mary wants to throw a can straight up into the air and then hit it with a second can. She wants the collision to occur at height h=10.0 m above the throw point. In addition, she knows that she needs t1=4.0 s between successive throws. … 
Classical Mechanics
Mary wants to throw a can straight up into the air and then hit it with a second can. She wants the collision to occur at height h=5.0 m above the throw point. In addition, she knows that she needs t1=4.0 s between successive throws. … 
Physics
Suppose you can throw a ball a maximum horizontal distance L when standing on level ground. How far can you throw it from the top of a building of height h = L if you throw it at 27.9 degrees? 
physics projectile  please help....
You are in an egg drop contest which you win by breaking your egg the hardest. You drop your egg off of a 3 story building (above the ground). You can throw it up with speed 11m/s, or straight down with speed 11 m/s. Ignoring air resistance, …