Wednesday

January 28, 2015

January 28, 2015

Posted by **Pratapveer** on Wednesday, September 18, 2013 at 5:02pm.

(a) How long it takes (in s) after the first can has been thrown into the air for the two cans to collide?

Δt=

- science -
**bobpursley**, Wednesday, September 18, 2013 at 5:43pmh first one: Vi*t-4.9t^2

h second one: Vi(t-4)-4.9(t-4)^2

because the heights are the same, set the equations equal, solve for t.

- science -
**Steve**, Wednesday, September 18, 2013 at 5:51pmIf 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,

vt-4.9t^2 = 5

t = 5/49 (v+√(v^2-98))

the 2nd can has been going up for only t-4 seconds, so

v(5/49 (v+√(v^2-98))-4)-4.9((5/49 (v+√(v^2-98)))-4)^2 = 5

v = 21.958 m/s ... call it 22m/s

Check:

22t-4.9t^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.

- science -
**Graham**, Wednesday, September 18, 2013 at 5:52pmLet 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 (Δt-t1) - g (Δt-t1)^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)*(Δt-t1) - g*(Δt-t1)^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

**Answer this Question**

**Related Questions**

Classical Mechanics - Mary wants to throw a can straight up into the air and ...

mitx 8.01x Classical Mechanics - Mary wants to throw a can straight up into the...

MITx: 8.01x Classical Mechanics - Mary wants to throw a can straight up into the...

Physics - Suppose you throw a stone straight up with an initial speed of 15.00 m...

math - You are standing on a bridge over a creek, holding a stone 20 feet above ...

Physics - A juggler throws a ball straight up into the air with a speed of 20. ...

physics - A juggler throws a ball straight up into the air with a speed of 11 . ...

science (physics) IV - anton plan that he can throw at a dart board from a ...

science - A cannon ball is fired straight up into the air at a speed of 80 ft/...

physics - Lance threw a ball straight up into the air. The ball's gravitational ...