## The Science behind the Warriors 3-Point Shots

What’s the science behind the amazing 3-point shooting of the Warriors Stephen Curry and Klay Thompson?

Klay Thompson throws a crisp pass to Stephen Curry, who launches a 3-point shot.  The ball follows a smooth, graceful arc before dropping through the hoop 28 feet away.

We should appreciate this simply for what it is: an awesome play by the Splash Brothers.  But science is all around us, so why not wonder about the science behind this feat of prowess?

The parabolic arc the ball follows is a result of the push Curry gives the ball and the force of gravity acting on it.  As the ball leaves Curry’s fingers it moves at an upward angle.  A physicist would say that the ball’s velocity has both a horizontal and vertical component; that is, the ball is moving both parallel to the floor and also in the up-down direction.

Once the ball is released, the only strong force acting on it is gravity.  (Air impedes the motion of the ball, but this effect is so small that it doesn’t significantly affect the motion.)  As a result of gravity, the ball’s vertical motion slows and slows until the ball hits the peak of the arc.  It is no longer going up.  Gravity continues to pull on it, so the ball begins to fall back to Earth, going downward faster and faster.

Gravity only pulls on things straight down.  So gravity can only affect the motion of the ball in the vertical direction; the horizontal motion of the ball remains unchanged during flight.  The combination of a constant horizontal motion with the ball slowing down then speeding up in the vertical direction results in the parabolic arc.

Curry releases a 3-pointer at an angle of about sixty degrees from the horizontal.  A basketball fan would say he’s got a lot of “arc” on the shot, which is not unusual for good ball players.  The higher the curved path of the ball, the closer to straight down it’s moving as it nears the hoop.  That gives the ball more clearance to get through the rim compared to a low-arcing shot.

For a 28-foot shot, Steph needs to impart a speed of about 30 feet per second – about 22 miles per hour – to get the ball to drop dead center through the hoop.

For a 28-foot shot, Steph needs to impart a speed of about 30 feet per second – about 22 miles per hour – to get the ball to drop dead center through the hoop.  And what precision!  If his release speed is off by less than one percent or if the angle is off by just a half a degree or so “clang,” the ball hits the rim.  No basket.

What about the spin that Curry gives the ball as it leaves his hand?  Although the spin of an object can affect its flight through the air – this is certainly true of a pitched baseball – the motion of a basketball is essentially unchanged by the amount of spin.  Then why do the best players launch their shots with just that right amount of spin?  A basketball released with spin is what players call a “soft shot.”  A soft shot is much less likely to bounce hard off the rim or backboard if it doesn’t swish through the net.

Does Curry’s long jumper almost look like it’s flying under its own power after he releases it?  There’s a good physics reason.  His shot is in the air for about one-and-a-half seconds.  Of that time, the ball spends a second above the height that is halfway up to the peak of the arc.  That means the ball spends most of its flight time higher up than its halfway mark, which creates the illusion that the ball is flying!

No basketball player – whether a middle schooler just learning the game or a professional like Klay Thompson or Steph Curry – thinks about shooting as a physics problem.  We probably shouldn’t either.  Instead, enjoy the beauty, the grace, the athleticism.  But once in a while it’s okay to wonder about the science too.

Share
Share