Is Speed the Same as Magnitude of Velocity in Horizontal Projectile Motion?

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SUMMARY

The discussion centers on the distinction between speed and magnitude of velocity in horizontal projectile motion. It clarifies that speed (a scalar) is not equivalent to velocity (a vector), emphasizing that the equation v = a*t applies only under specific conditions, such as constant acceleration and zero initial velocity. The correct formulation for the velocity in this context is |v| = √(v_0^2 + g^2(2h/g)), where g represents gravitational acceleration and h is the height of the projectile. The conversation also highlights the importance of understanding the units involved in these calculations.

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This is a horizontal projectile problem off a building.

Is the speed of an object equal to:

##v=a*t##
or
##v = |v|## (magnitude)

Current problem:
##Velocity = √(v_0^2 + g^2(2h/g)) positive below x axis##

##t = √(2h/g)##

so is the speed suppose to be ##v = g√(2h/g) m/s##

or is it suppose to be

##|v| = √(v_o^2 + g^2(2h/g)) m/s##
 
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v=at is true only if the acceleration is constant and the initial velocity is zero, it is not true in your case. You can use it for one velocity component (but not the full velocity) here.

v and |v| are different objects (vector and scalar), you cannot compare them with an equal sign.

v = g√(2h/g) m/s
The "m/s" there does not make sense. The units are in g and h.

or is it suppose to be
Please post the full problem statement, if you have questions how to interpret it.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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