Rocket tosses the foam ball three ways on the lawn: low and flat, medium, then almost straight up.
"The high one went up forever," he says, "but it landed almost at my feet."
Raven marks each landing with tape. "What do you notice? The middle toss went the farthest."
"And the flat one came down too soon," Rocket says. "So there is a best angle."
Nova hovers over the middle marker. "A physics text has a number for that angle," she says. "Can you guess it?"
Rocket squints at the sky. "Halfway between flat and straight up?"
Nova hums, which is her yes. "Now find out why, and what a harder throw does."
The horizontal distance a projectile travels on level ground is called its range.
A physics text says the greater the initial speed, the greater the range for a given launch angle.
Height grows even faster. NASA explains that the maximum altitude changes as the square of the launch speed.
Doubling the launch speed produces four times the maximum altitude. Throw twice as fast, and the ball rises four times as high.
The flight depends only on launch speed and gravity. The size, shape and mass of the ball do not appear in NASA's flight equations.
In purely ballistic flight, with no air, all objects fly the same way.
The launch angle has a dramatic effect on range. For a fixed speed, the greatest range comes at 45 degrees, halfway between flat and straight up.
That is true only when air resistance is ignored. With air resistance, the best angle is about 38 degrees.
For every angle except 45 degrees, there are two angles that give the same range. The two angles add up to 90 degrees.
A ball launched at 15 degrees and one launched at 75 degrees land in the same spot. The 75 degree ball flies much higher and stays up longer.
| Launch angle | Height of the arc | Range (same speed, no air) |
|---|---|---|
| 15 degrees (low and flat) | low | medium |
| 45 degrees (halfway up) | medium | the farthest |
| 75 degrees (steep) | high | medium, the same as 15 degrees |
| 90 degrees (straight up) | the highest | zero, it lands where it started |
| Statement | True or false? |
|---|---|
| A faster launch gives a longer range at the same angle. | ? |
| A ball tossed straight up lands far away. | ? |
| In ballistic flight with no air, a heavy ball and a light ball fly the same path. | ? |
| Air resistance makes the best angle for range a little flatter than 45 degrees. | ? |
Sharp reasoning. Tomorrow is Field Lab: three launch angles, nine gentle tosses, one tape measure.