Second Unit Summary
Free Fall:
If a ball was dropped from any height, (neglecting air resistance) the ball will accelerate 10m/s^2 due to gravity, and the equation (d=1/2gt^2) helps you figure out the time it is in the air or the height it was dropped from. So for example if a ball was dropped from an unknown height and it took the ball 3 seconds to hit the ground, how high was it dropped from. d=1/2(10)*(3^2), d=5*9, d=45m
Projectile motion:
If something is thrown off a cliff at an angle (not only downwards but sideways as well) their are two velocities (horizontal / vertical) in affect here. To find exactly where the ball will drop, you first must find the time it is in the air, to do that you have to work on the vertical drop alone. You use the (d=1/2gt^2), then when you get the time, you can also find out the horizontal distance by using this equation (v=d/t) or (d=vt)
For example if you have a cliff that is 80 meters tall and you throw a ball from the top of it with a horizontal velocity of 20m/s where will it land?
d=1/2gt^2, 80=5t^2, 16=t^2, t=4seconds.
Now you can find the horizontal velocity. d=Vt, d= 20*4, d=80m
Throwing things up at an angle:
The time it takes the ball to go up is it exactly the same time it needs to go down, and the ball always accelerates downwards at 10m/s^2. for example if a ball was thrown upwards with a velocity of 30m/s, it would take 6 seconds for it to hit the ground, this is because the first second, it would be moving upwards but has a velocity of 20m/s, the 2nd second the ball will be moving upwards with 10m/s, the 3rd second it would be at the top of it's path with 0m/s, the 4th second it would be going downwards now with 10m/s, the 5th second going downwards with 20m/s, and the sixth second it would hit the ground with 30m/s.
Newton's 2nd law:
The time it takes the ball to go up is it exactly the same time it needs to go down, and the ball always accelerates downwards at 10m/s^2. for example if a ball was thrown upwards with a velocity of 30m/s, it would take 6 seconds for it to hit the ground, this is because the first second, it would be moving upwards but has a velocity of 20m/s, the 2nd second the ball will be moving upwards with 10m/s, the 3rd second it would be at the top of it's path with 0m/s, the 4th second it would be going downwards now with 10m/s, the 5th second going downwards with 20m/s, and the sixth second it would hit the ground with 30m/s.
Newton's 2nd law:
"Acceleration is directly proportional to Force and is inversely proportional to mass"
If there was a cart that had a string attached on it then to a hook that is playing the role of the force
If the mass of the cart was increasing and the mass of the hook was decreasing, the acceleration of the cart will decrease as mass is inversely proportional to acceleration. But if the mass of the system was kept the same and the mass on the cart was added to the hook, the acceleration would increase, as force is directly proportional to force (a=f/m) (w=mg)
Skydiving:
When jumping off an airplane (with a parachute) the only 2 things affecting your air resistance is the speed that you are travelling at downwards and the surface area you have. When you jump you start the build up speed so that means air resistance also increases which decreases your acceleration downwards. when you hit the first terminal velocity this means that you are going your fastest and that the air resistance it equal to the force of your weight, so your velocity is constant now. As soon as you pull the parachute, the upwards force of air resistance rockets and the weight stays the same, so the acceleration is going upwards, you are still moving downwards but slowing down. after the parachute has been open your force of air resistance slowly decreases as the speed is decreasing, trying to equalize with the weight of the person. When it is equal you hit another terminal velocity, which means that you don't accelerate any more, and the velocity is constant due to the air resistance and the weight being equal. There is one difference between the first terminal velocity and the second, it is that the first is faster (greater velocity) than the second
If the mass of the cart was increasing and the mass of the hook was decreasing, the acceleration of the cart will decrease as mass is inversely proportional to acceleration. But if the mass of the system was kept the same and the mass on the cart was added to the hook, the acceleration would increase, as force is directly proportional to force (a=f/m) (w=mg)
Skydiving:
When jumping off an airplane (with a parachute) the only 2 things affecting your air resistance is the speed that you are travelling at downwards and the surface area you have. When you jump you start the build up speed so that means air resistance also increases which decreases your acceleration downwards. when you hit the first terminal velocity this means that you are going your fastest and that the air resistance it equal to the force of your weight, so your velocity is constant now. As soon as you pull the parachute, the upwards force of air resistance rockets and the weight stays the same, so the acceleration is going upwards, you are still moving downwards but slowing down. after the parachute has been open your force of air resistance slowly decreases as the speed is decreasing, trying to equalize with the weight of the person. When it is equal you hit another terminal velocity, which means that you don't accelerate any more, and the velocity is constant due to the air resistance and the weight being equal. There is one difference between the first terminal velocity and the second, it is that the first is faster (greater velocity) than the second
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