Show full work and details and answer please. Best correct answer gets 1,500 poi

Question

Show full work and details and answer please. Best correct answer gets 1,500 points

Spade and Archer, each on a sled, are stranded in the middle of a frozen lake. They get the idea to toss something at each other in hopes of getting off the lake. The only thing they have is their golden, jewel-encrusted, 4.00-kg falcon statuette. Suppose Spade and his sled and Archer and his sled each have the same total mass of 80.00 kg. Spade initially has the falcon, and tosses it towards Archer, who immediately tosses it back to Spade. If each toss results in a (constant) horizontal velocity of 2.00 m/s (measured with respect to the lake) for the falcon, what is the speed of each after Spade catches the falcon?

Explanation / Answer

the velocity of their center of mass=0
so as there is no external force, the velocity of center of mass will remain the same.

now step 1:
spade tosses the falcon.
now once the falcon is tossed away, falcon gets a speed of 2 m/s, towards archer.

then spade will be propelled backwards with a speed v m/s

conserving linear momentum:
80*v=4*2

v=0.1 m/s, w.r.t. the lake..

now when archer catches the falcon, let the net speed of the falcon+archer be v1, to the right.

then by keeping velocity of center of mass 0,

mass of spade*spade's speed+mass of (archer+falcon)*their speed=0

80*0.1=(80+4)*v1

v1=0.095 m/s, to the right side

now step 2:

when archer throws the falcon:
let speed of archer's slade be v2 after the falcon is released.

then conserving momentum before and after the thrwoing of falcon:

84*0.095=80*v2-4*2

v2=0.2 m/s.towards right

now when spade catches the falcon, by conserving the velocity of the center of mass:

(80+4)*v=80*0.2
v=0.1904 m/s, to the left

where v is the speed of spade's slade afte rcatching

so final answer:

spade moves with 0.1904 m/s. to the left

archer moves with 0.2 m/s to the right

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