The physics and science of falling balls
As a simple argument for that result, think about the ball’s speed as it falls: it starts from rest and, over the course of 1 second, it acquires a downward speed of 9.8 m/s. Its average speed during that first second is half of 9.8 m/s or 4.9 m/s. And that is just how far the ball falls in that first second: 4.9 m. By holding the ball 4.9 m above the floor, you can arranged for it to hit one second after you drop it.
Yes! If you are walking east and you come to a stop, it is because you accelerated to the west! By "deceleration" we mean acceleration in the direction opposite our direction of motion. Thus in a car, when you stomp on the brake and decelerate, you are actually accelerating toward the rear of the car (in the direction opposite its direction of motion).
Actually, as you stand on the end of the board or as you push off from its end, you are pushing on the board and it is pushing back on you. The forces you exert on one another are exactly equal in amount but opposite in direction. That observation is called Newton’s third law of motion and is the real meaning behind the phrase “for every action there is a reaction.”
What you mean by “changes direction” is that the direction part of its velocity changes. For example, instead of heading east at 10 m/s (or 10 miles-per-hour, if that feels more comfortable), it heads north at 10 m/s (or 10 miles-per-hour). This change in direction involves acceleration. The car must accelerate toward the west in order to stop heading east, and it must accelerate toward the north in order to begin moving north. Actually, it probably does both at once, accelerating toward the northwest and shifting its direction of motion from eastward to northward.
Yes to the first part, no to the second part. Remember that acceleration can change the direction of velocity without changing the magnitude of velocity (the speed of the object). When the space shuttle accelerates, its speed doesn’t change, only its direction of travel. Although it accelerates endlessly, it never goes faster or slower. Actually, if the shuttle’s orbit isn’t circular, its speed does increase and decrease slightly as it orbits the earth in an ellipse, but that’s an unimportant detail. For a circular orbit, the shuttle’s speed is constant but its velocity (speed and direction) is not constant!
If you shot the bullet horizontally, it really would hit the ground at the same time as the bullet you simply dropped. During the firing, the bullet would accelerate like crazy, but only horizontally. It would leave the gun with a velocity that was only in the horizontal direction. With no forces pushing on it horizontally after that (we’ll neglect air resistance), the bullet will make steady progress downfield. But at the same time, it will begin to fall. The vertical component of its velocity will gradually increase in the downward direction as it falls. Like the dropped bullet, it will drift downward faster and faster and the two will hit the ground together.
The 45° angle is ideal because it gives the ball a reasonable upward component of velocity and also a reasonable downfield component of velocity. The upward component is important because it determines how long the ball will stay off the ground. The downfield component is important because it determines how quickly the ball will travel downfield. If you use too much of the ball’s velocity to send it upward, it will stay off the ground a long time but will travel downfield too slowly to take advantage of that time. If you use too much of the ball’s velocity to send it downfield, it will cover the horizontal distances quickly but will stay of the ground for too short a time to travel very far. Thus an equal balance between the two (achieved at 45°) leads to the best distance. Note that this discussion is only true in the absence of air resistance.
The bullet accelerates gradually, like everything else. However, the forces that push on the bullet when the gun is fired are extremely large and it accelerates extremely rapidly. It goes from 0 to maximum speed in about a thousandth of a second.
When the space shuttle circles the earth, it’s experiencing only one force: the force of gravity. As a result, it’s perpetually accelerating toward the earth’s center. If it weren’t moving initially, it would begin to descend faster and faster until…splat. But it is moving sideways initially at an enormous speed. While it accelerates downward, that acceleration merely deflects its sideways velocity slightly downward. Instead of heading off into space, it heads a little downward. But it never hits the earth’s surface. Instead, it arcs past the horizon and keeps accelerating toward the center of the earth. In short, it orbits the earth—constantly accelerating toward the earth but never getting there.
The answer to this puzzle lies in the definition of force. How would you measure the amount of a force? Well, you would push on something with a known mass and see how much it accelerates! Thus this relationship (Newton’s second law) actually establishes the scale for measuring forces. If your second relationship were chosen as the standard, then all the forces in the universe would simply be redefined up by a factor of two! This redefinition wouldn’t harm anything but then Newton’s second law would have a clunky numerical constant in it. Naturally, the 2 is omitted in the official law.