#Soccer #Players #Bend #Shots #Midairphysics,forces,sports,soccer,world cup 2026">How Can Soccer Players Bend Their Shots in Midair?
We need one more thing—how about Newton’s second law? This says the acceleration depends on the net force (Fnet) and the mass (m) of an object. It’s usually written as Fnet = m × a, but we can rearrange it like this: a = Fnet/m. Combining this with our gravitational force, we get something pretty interesting:
Courtesy of Rhett Allain
Since both gravity and acceleration depend on the mass of the ball, the mass cancels. We find that any object on Earth has a downward acceleration of 9.8 meters per second per second (m/s2). This means that if you drop a bowling ball and a marble at the same time, they’ll hit the ground at the same time—even though the gravitational force on the bowling ball is thousands of times higher. Weird, right?
Anyway, now, in the presence of gravity, if you kicked a ball at an upward angle, it’s vertical velocity would slow, halt, and reverse, with the speed increasing as it falls. In other words, it starts accelerating in the downward direction as soon as it’s kicked, even while it’s moving upward.
What about the horizontal motion? Ah, since there’s no horizontal force after the initial kick, the ball continues traveling forward at the same speed, just like in space. People tend to think a ball falls because its forward motion slows, but actually it’s the opposite. Without air drag it doesn’t slow down at all. It only stops because the ground gets in the way.
So what we get for a trajectory is that familiar upside-down parabola, often called a ballistic trajectory because it’s the path of any unpowered projectile, like a cannon ball, a bullet, or a basketball. Any flying object for which gravity is the only (significant) force acting on it will move this way.
Soccer With Air
Happily, the Earth does have air. But it drastically changes the game. Now there is a continuous force acting horizontally, which we call air resistance, or drag, and it pushes in the direction opposite to the ball’s motion.
Think of air molecules as a bunch of tiny ping-pong balls. As a soccer ball moves through the air it collides with gazillions of these little air balls, and each collision exerts a backward-pushing force; all combined, this creates the total air-resistance force. The bigger the object, the more collisions it has to fight through.
#Soccer #Players #Bend #Shots #Midairphysics,forces,sports,soccer,world cup 2026
We need one more thing—how about Newton's second law? This says the acceleration depends on…
#Astronauts #Fast #Theyredot physics,physics,astronomy,space,spacecraft,moon landing,navigation,acceleration">How Can Astronauts Tell How Fast They’re Going?
Let’s use our car again, but this time we’ll get real numbers from the accelerometer in our smartphone. Say we start at a red light and then accelerate at 2 m/s2 (meters per second squared) for five seconds. From the equation above, Δv1 would be 2 x 5 = 10 m/s, so that’s our velocity. Now, after cruising for a while, we accelerate again at 1 m/s2 for five more seconds. Δv2 is then 1 x 5 = 5 m/s. Adding these two changes, our velocity is now 15 m/s. And so on.
The only problem is that inertial measurement isn’t as accurate as the Doppler method over long periods, because small errors will keep accumulating. That means you need to recalibrate your system periodically using some other method.
Optical Navigation
On Earth, people have long navigated by the stars. In the northern hemisphere, just find Polaris. It’s called the North Star because Earth’s axis of rotation points right at it. That’s why it appears stationary, while the other stars seem to revolve around it. If you point a finger at Polaris you’ll be pointing north, and you can use that orientation to go in whatever direction you want.
Now, if you can measure the angle of Polaris above the horizon, you’ll also know your latitude. If the angle is 30 degrees, you’re at latitude 30 degrees. See, it’s easy. And once you can measure position, you just need to do it twice and record the time interval to find your velocity.
But celestial navigation works because we know how the Earth rotates, and that doesn’t help in a spacecraft. Oh well, can we just use the stars like you would use the cows on the side of the road? Nope. The stars are so far away, astronauts would need to travel for many, many generations to detect any shift in their position. Like the airplane flying over the sea, you’d seem to be stationary, even while traveling 25,000 mph.
But we can still use the basic idea. For optical navigation in space, a spacecraft can locate other objects in the solar system. By knowing the precise location of these objects (which change over time) and where they appear relative to the viewer, it’s possible to triangulate a position. And again, by taking multiple position measurements over time, you can calculate a velocity.
In the end, even though spaceships lack speedometers, it’s possible to track their speed indirectly with a little physics. But it’s just another example of how flying in space is really, totally different—and way more complicated—than driving or flying on Earth.
