Ellyn throws a dart at a speed v into a thick dartboard. It penetrates a distanc

ID: 1641732 • Letter: E

Question

Ellyn throws a dart at a speed v into a thick dartboard. It penetrates a distance x.

(a) If she wants the dart to penetrate twice as far, how fast does it have to be thrown?

(b) How far would the dart penetrate if thrown at twice its initial speed? Why are your answers different?

(c) A dart thrown at 3.2 m/s penetrates 0.9 cm into the dart board. Calculate the speed of a dart that would penetrate 1.8 cm into the dartboard.

(d) Calculate how far the same dart would penetrate if it were thrown at 6.4 m/s

final velocity = 0

initial velocity=v

we got

v^2=-2ax=>a=-v^2/2x

now for x to be 2x ,let velocity is v'

v'^2=(2*v^2/2x)*2x=sqrt(2)v

so velocity=1.414v

(v) if v'=2v

x'=v'^2/2a=4v^2/(2*v^2/2x)=4x

so 4 times

so velocity=1.414*3.2=4.52 m/s

(d) if v=6.4 m/s

x=4*0.9=3.6 cm

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