Projectile Motion
Split the launch velocity into horizontal and vertical parts, then run constant velocity across and constant acceleration downwards, with time as the only quantity the two share. Range, greatest height and flight time follow.
What a learner can do afterwards
- Split a launch speed and angle into horizontal and vertical components
- Find the time of flight from the vertical motion, then the range from the horizontal
- Say what the model assumes by leaving air resistance out
1 · Read
Kick a ball into the air and split its flight in two: sideways and up-and-down. Split the launch into v cos(theta) across and v sin(theta) up: 25 m/s with cos 0.8 and sin 0.6 gives 20 across and 15 up. Then run two independent lives: constant velocity across, constant acceleration down, with time the only quantity both share.
With vertical speed 15 m/s and g = 10, rising takes 15/10 = 1.5 s and symmetric flight doubles it to 3 s. Range is horizontal speed times time: 20 times 3 = 60 m. Greatest height uses v squared = u squared + 2as with v = 0: 225/20 = 11.25 m.
At the very top the vertical velocity is zero, the instant rising turns to falling. With no air resistance nothing pushes across, so horizontal velocity stays constant all flight. The model assumes gravity alone: no drag, constant g, flat ground. Because real drag slows the ball, leaving it out makes the predicted range too long.
Real drag bites hardest at speed and steals range, so ignoring it overestimates how far the ball lands. The same steps handle 20 m/s at 30 degrees: vertical 10 m/s gives 2 s of flight, and 17.32 m/s across gives about 34.6 m. State the assumptions to show where the maths ends and the world begins.
Split the launch into across and up, time the vertical life, then spend that time crossing.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.