Physics 1 — Motion & Energy

Projectile motion

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: launch something at an angle and the motion splits into two independent stories: sideways, the speed never changes; up-and-down, it's pure free fall. The two only share one thing — the clock. That's why a bullet fired level and one dropped from the same height hit the ground at the same time.

v_{launch} = 20

launch speed (m/s)

\theta := 35 deg

= 35 deg launch angle

R_{range} = \frac{v_{launch}^{2} \cdot \mathrm{sin}\left(2 \cdot \theta\right)}{9.81}

38.3157

horizontal range (m)

h_{max} = \frac{\left(v_{launch} \cdot \mathrm{sin}\left(\theta\right)\right)^{2}}{2 \cdot 9.81}

6.7072

peak height (m)

x * tan(theta) - 9.81 * x^2 / (2 * (v_launch * cos(theta))^2)

the flight path y(x) — a parabola

Real-world hook: the range formula aims basketball shots, water-fountain arcs, and artillery.

Try it yourself: which launch angle gives the maximum range?

Show the answer

45° — because range ∝ sin(2θ), which peaks when 2θ = 90°. (And 30° and 60° land in the same spot, since sin is symmetric about 90°.)