In the first passage of Section 1 of TBR's Physics book, there is a figure of Galileo tossing stones from the top of a rocket. In the explanation to Q#1, it says that acceleration in the y-direction is minus-g. Why is it minus-g if the rock is going to be increasing its acceleration as it is being thrown from the rocket to the surface? I thought minus-g is used when tossing a projectile upwards and against the force of gravity.
What general rule can I take in regards to determining the sign for "g"?
As MBHockey mentioned, the sign convention is not necessary in many problems, as long as you define two opposite directions with opposite signs.
The question is as follows:
- Of the two tosses done on Earth, A and B, which one stays in the air longer?
A. Stone A remains in flight longer.
B. Stone B remains in flight longer.
C. Both stones remain in flight for the same amount of time.
D. The time varies with the radius of the stone.
The difference in the question lies the initial velocity of the two trials. Stone A and Stone B both have masses of 1.0 kg and are thrown horizontally from a height of 20 meters with different initial speeds.
Because time of flight depends on the y-direction and both stones are thrown horizontally (with no y-velocity), we can ignore the x-component of this question. In essence, it would be the same question if both stones were dropped straight down.
Whether we define g as 9.8 m/s2 or -9.8 m/s2, it is the same for both stones. Both stones travel the same distance, experiencing the same g, and having the same initial y-direction speed (0), so they each experience the same y-component and thus hit at the same time.
It's exactly as MBHockey explained it "If you shoot a bullet at the same instant that you drop a bullet from the same height they will both hit the ground at the same time. When you shoot a bullet, it's not like it waits until its initial horizontal velocity slows down for it to start falling toward earth (contrary to Wile E. Coyote physics)." And he brings up a wonderful point that cartoons by Warner Brothers often are sources of faulty physics. However, Hannah Barbera cartoons have not been analyzed for physical realism.
As for your question about the sign of g, let's start with the idea that the flight time needs to be a
positive value. That is a must according to our conventions.
The kinematics equation of choice here is
deltah = 0.5 at
exp2 + v
ot
deltah = 0.5 at
exp2 + v
ot
deltah = 0.5 at
exp2 + 0
(2 x
deltah)/g = t
exp2
From here, it's your choice as to what signs to use. If you say it fell 20 meters, then
deltah = -20. In order to have the time be a positive value (and for square roots to be
real), we need to use -9.8 m/s2 for g. The math tells is that the flight time when dropped or thrown horizontally from a height of 20 meters is square root of 4 (square root of 40/10), or about 2 seconds for any object in the absence of wind resistance.
