NEXT STEP's Physics and Math content review buoyancy question???

[nai54]

Hi so the question is on page 491 number 49. It says:

A child swims to the bottom of a swimming pool holding two toys. One is a plastic dog with a density of 0.2g/cm^3 and the other is a model truck of density 0.4g/cm^3. The child releases both toys. Which of the following is true regarding their accelerations?

A. The dog accelerates more quickly.
B. The truck accelerates more quickly.
C. They accelerate at equal rates.
D. Acceleration depends on depth.

I thought it would be B because the truck has a greater density therefore a greater buoyancy force so it should accelerate more, but the answer is A. Does anybody mind explaining this ? Thanks!

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[dahmsom]

@nai54
Just remember lighter density objects accelerate faster. I will u show u mathematically why. Since it's completely submerged at first the volume of the object and the displaced fluid are equal. Once you solve for acceleration you will see that acceleration is equal to g(density of water - density of object) / density of object . To keep acceleration high and fast ,the numerator has to be big, therefore the density of object has to be small. Hope this helps

 

[nai54]

thank you!

 

[theonlytycrane]

One thing to note: this calculation assumes that the dog and the truck have the same volume.