Projectile range
Launch something at an angle - a football, a water-balloon, a long jump - and
physics can tell you exactly where it lands. For a launch over flat ground
(ignoring air resistance), the range formula is:
R = v^2 * sin(2 * angle) / g
v = launch speed, in m/s
angle = launch angle above the ground
g = 9.8 m/s^2
The sin(2 * angle) is the interesting part: it peaks when 2 * angle is
90 degrees, which is why 45 degrees is the maximum-range angle - and why a
35-degree launch and a 55-degree launch land in the same spot.
One practical trap: sin() here expects radians, not degrees. A degree
angle has to be converted inside the expression by multiplying by PI/180.
Forget the conversion and sin(70) quietly computes the sine of 70 radians -
a completely different (and wrong) number, with no error to warn you.
The starter shows the shape for a 10 m/s launch at 45 degrees. This lesson's
launch is faster and flatter.
Your task: a ball is launched at 20 m/s, at 35 degrees above the ground.
How far away does it land? (g = 9.8)
You'll practice:
- Substituting into a formula with a trig function
- Converting degrees to radians inline with * PI/180