What is the deceleration of the vehicle?

Classical Mechanics Level 3

It is noted that while stopping, the water surface in a glass of water sitting in the cup holder of a car is slanted at an angle of 1 5 ∘ 15^\circ relative to the horizontal street. What is the rate at which the car is decelerating?

-8.63 ft/s^2 -4.63 ft/s^2 -7.63 ft/s^2 -10.63 ft/s^2

Jaber Al-arbash by Jaber Al-arbash , 28, USA

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1 solution

Jaber Al-arbash
Feb 14, 2016

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Should it not be g/Tan15??

Emer Brady - 5 years, 3 months ago

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You're thinking of it in terms of the fact that the acceleration has a component for 'g' that points downward and 'a' that points horizontally with the tan function being equal to opposite/adjacent (vertical/horizontal), but the effect of 'g' on the water is essentially to reduce the angle relative to the horizontal and the effect of 'a' is to increase the angle. Also if you try g/tan15 you end up with a result that says the car is decelerating at nearly 3 g's, which should seem suspicious by juxtaposition with every day experience, or by comparison with the fact that an acceleration of 1 g would result in an angle of 45 degrees.

Tristan Goodman - 2 years, 5 months ago

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