If a projectile released or hit at a 45° angle above horizontal should go th…

If a projectile released or hit at a 45° angle above horizontal should go the farthest, then why, in the game of golf, does the three iron (20° loft) hit a golf ball so much farther in the air than, say, a seven iron (approximately 45° loft) if the same technique and force are produced by the golfer? Is it backspin, shaft length, etc.?

It’s backspin! Air pushes the spinning ball upward and it flies downfield in much the same way as a glider. When you throw a glider for distance, you concentrate your efforts on making it move horizontally because the air will help to keep the glider from hitting the ground too soon. Similarly, the air holds the spinning golf ball up for a remarkably long time so that giving the ball lots of downfield speed is most important for its distance. That’s why a low-loft club like a three iron sends the ball so far.

Is it possible for a skydiver who jumps second from a plane to put himself in an…

Is it possible for a skydiver who jumps second from a plane to put himself in an aerodynamic position and overtake a person who jumped first?

Yes. When you skydive, your velocity doesn’t increase indefinitely because the upward force of air resistance eventually balances the downward force of gravity. At that point, you reach a constant velocity (called “terminal velocity”). Just how large this terminal velocity is depends on your shape. It is possible to increase your terminal velocity by rolling yourself into a very compact form. In that case, you can overtake a person below you who is in a less compact form.

Why does a ball fall 4.9 meters during its first second of falling?

Why does a ball fall 4.9 meters during its first second of falling?

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.

If force causes only acceleration and not velocity, does a machine (i.e. an engi…

If force causes only acceleration and not velocity, does a machine (i.e. an engine) that causes a constant velocity in an adjacent object not exert a force?

If that adjacent object is free of any other forces, then no, the machine does not exert a force on it! This is a wonderful question, because it points toward many of the issues concerning energy and work. The bottom line is this: if some object is truly free moving (no other forces on it), it will move along at constant velocity without anything having to push on it. For example, if your car were truly free moving (no friction or air resistance), then it would coast forever on a level surface and the engine wouldn’t have to do anything. You could even put the car in neutral and turn off the engine. The only reason that you need an engine to keep pushing the car forward is because friction and air resistance push the car backwards.

Is there a fixed amount of force in the universe?

Is there a fixed amount of force in the universe?

No, forces generally depend on the distances between objects, so that two objects that are moving together or apart will experience different amounts of force as they move about. As a result, the total amount of force anywhere can change freely. But there are quantities that have fixed totals for the universe. The most important of these so-called “conserved” quantities is energy.