Studying formulas about velocity and acceleration I came up with a question: if I throw an object in the air with a velocity v0 (suppose i throw it vertically) in how much time its final velocity vf will reduce to 0 due to the force go gravity? Here is how I tried to solve the problem:
Calculation of the time
I know that the final velocity of a object that receive an acceleration is: vf=v0+at where a is the acceleration and t is the time in which the acceleration acts. I supposed that vf after a negative acceleration (the gravitational acceleration on Earth g) will reduce to 0 and so I set up the following equation: 0=→v0−→g⋅t and solving the equation for t I got that t=v0g
Calculation of the space
I know that the formula to calculate the space that is made by an object moving with an acceleration is S=v0t+12at2 But now I can apply (1) to the equation: S=v0⋅v0g−12g(v0g)2 S=v20g−v202g=v202g That would be the formula for the space.
Reassuming an object thrown in the air with a velocity v will stop moving in the air after a time t=vg after making a distance S=v22g.
Is this correct?
Answer
Yes, that's how physics is done!
Aside from what I assume is a typo in your final summary, your equations (1) and (2) are both correct. You should note, however, that this is the Newtonian Way of answering your questions. Real-life experiments will show some variation in time and distance traveled, a quicker slow-down time, and a shorter path. This is due to air resistance.
You'll need a more complex model if you want super-accurate answers, but these should work for rough estimations and low-level physics classes.
No comments:
Post a Comment