Question

a darts player is throwing new darts at a target to test them out. masses of darts color mass (g) blue 24 green 21 gold 30 red 18 silver 25 the player applies the same force to each dart as she is throwing it. order the colors of the darts to show the size of the acceleration each dart will have as it is being thrown. larger acceleration blue green gold red silver smaller acceleration

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Rearranging for acceleration gives \(a=\frac{F}{m}\). Since the force \(F\) is the same for all darts, acceleration \(a\) is inversely proportional to mass \(m\) (\(a\propto\frac{1}{m}\)).

Step2: Compare the masses

The masses of the darts are: blue (\(m = 24\space g\)), green (\(m = 21\space g\)), gold (\(m = 30\space g\)), red (\(m = 18\space g\)), silver (\(m = 25\space g\)).

Step3: Order based on inverse - mass relationship

Since \(a\propto\frac{1}{m}\), the order of acceleration (from larger to smaller) is based on the order of mass (from smaller to larger). The order of masses from smallest to largest is: red (\(18\space g\)) < green (\(21\space g\)) < blue (\(24\space g\)) < silver (\(25\space g\)) < gold (\(30\space g\)).

Answer:

red, green, blue, silver, gold