Question

acrobats are being thrown by a catapult during a performance.
names of acrobats
acrobat name mass (kg)
brandon 84
laxi 82
trevor 81
monica 85
darnel 78
the catapult applies the same force to each acrobats feet. order the names of the acrobats to show the size of the acceleration the acrobats will have as they are being thrown.
larger acceleration
brandon
laxi
trevor
monica
darnel
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 acrobats, acceleration \(a\) is inversely proportional to mass \(m\). That is, \(a\propto\frac{1}{m}\).

Step2: Compare the masses

We have the masses: Brandon (\(m = 84\space kg\)), Laxi (\(m = 82\space kg\)), Trevor (\(m = 81\space kg\)), Monica (\(m = 85\space kg\)), Darnel (\(m = 78\space kg\)).

Since \(a\propto\frac{1}{m}\), the smaller the mass \(m\), the larger the acceleration \(a\).

Ordering the masses from smallest to largest: \(78<81 < 82<84<85\)

Step3: Order the acrobats based on acceleration

Based on the inverse - relationship \(a\propto\frac{1}{m}\), the order of acrobats from larger acceleration to smaller acceleration is: Darnel (mass \(78\space kg\)), Trevor (mass \(81\space kg\)), Laxi (mass \(82\space kg\)), Brandon (mass \(84\space kg\)), Monica (mass \(85\space kg\))

Answer:

larger acceleration: Darnel, Trevor, Laxi, Brandon, Monica : smaller acceleration