Physics Problem – Projectile Motion A soccer ball is kicked from ground level with an initial speed of 25 m s⁻¹ at an angle of 30° above the horizontal. Neglect air resistance and assume the ground is flat. How long is the ball in the air before it lands? What is the maximum height it reaches? How far horizontally does it travel before hitting the ground?Solution Time of flight The vertical component of the initial velocity isv0y=v0sinθ=25sin30∘=25×0.5=12.5 m s−1 The total time in the air satisfies vy=v0y−gt=0 at the peak, and the full flight is twice that time: tflight=g2v0y=9.82×12.5≈2.55 s Maximum height Using h=2gv0y2:h=2×9.8(12.5)2≈19.6156.25≈7.98 m Horizontal range The horizontal component isv0x=v0cosθ=25cos30∘=25×0.8660≈21.65 m s−1 Range (R = v_{0x} , t_{\text{flight}} \approx 21.65 \times 2.55 \approx 55.2\ \text{m} ] Dive deeper:
