Certain mushrooms launch their spores by a catapult mechanism. Aswater condenses

Question

Certain mushrooms launch their spores by a catapult mechanism. Aswater condenses from the air onto a spore that is attached to themushroom, a drop grows on one side of the spore and a film grows onthe other side. The spore is bent over by the drop's weight, but when the film reaches the drop, the drop's water suddenlyspreads into the film and the spore springs upward so rapidly thatit is slung off into the air. Typically, the spore reaches a speedof 1.6 m/s in a 5.0 ?m launch; its speed is then reduced tozero in 1.0 mm by the air. Using that data and assuming constantacceleration, find the acceleration in terms of g during(a) the launch and (b) the speed reduction. I thought maybe for part A you would plug 1.6 m/s for initialvelocity and 5.0x10^-6 m for displacement in thisconstant acceleration formula, but you don't have the time. Andsame for part B. D = vit+1/2at^2

Explanation / Answer

      (a)               Initial velocity, Vi = 0               Final velocity, Vf =1.6 m/s               Distance , S = 5 X 10 -6 m               Vf 2 - Vi 2 = 2 a S                1.6 2 - 0 2 = 2 a * 5 X 10 -6                    2.56 = 10 -5 a                Acceleration, a = 256000 m/s^2                                      = ( 256000 / 9.8 ) g                                      = 26100 g       (b)                                 Initial velocity, Vi = 1.6m/s               Final velocity, Vf = 0               Distance , S = 0.001 m               Vf 2 - Vi 2 = 2 a S                0 2 - 1.6 2 = 2 a * 0.001                    - 2.56 = 0.002 a                Acceleration, a = - 2.56 / 0.002 m/s^2                                       = - 1280 m/s^2                                      = ( - 1280 / 9.8 ) g                                      = - 130 g

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