A plane traveling horizontally at 150 m/s drops a package from 1.3 km altitude. The package travels horizontally about 1,620 meters before hitting the ground.

This classic projectile motion problem separates horizontal and vertical components, as there's no horizontal acceleration but gravity acts downward.

Key Assumptions

  • Acceleration due to gravity: g=9.8 m/s2g=9.8,\mathrm{m/s^2}g=9.8m/s2.
  • No air resistance.
  • Package inherits the plane's horizontal velocity (150 m/s) upon release; initial vertical velocity is 0 m/s.
  • Altitude: 1,300 m (converted from 1.3 km).

Step 1: Time of Fall

Vertical motion is free fall:
h=12gt2h=\frac{1}{2}gt^2h=21​gt2
1300=12(9.8)t21300=\frac{1}{2}(9.8)t^21300=21​(9.8)t2
t2=26009.8≈265.306t^2=\frac{2600}{9.8}\approx 265.306t2=9.82600​≈265.306
t≈16.29 st\approx 16.29,\mathrm{s}t≈16.29s.

Step 2: Horizontal Distance

Horizontal motion is constant velocity:
dx=vxt=150×16.29≈2443.5 md_x=v_xt=150\times 16.29\approx 2443.5,\mathrm{m}dx​=vx​t=150×16.29≈2443.5m No, wait—recalculate precisely:
t=2×13009.8=265.3061=16.29 st=\sqrt{\frac{2\times 1300}{9.8}}=\sqrt{265.3061}=16.29,\mathrm{s}t=9.82×1300​​=265.3061​=16.29s
dx=150×16.29=2,443.5 md_x=150\times 16.29=2,443.5,\mathrm{m}dx​=150×16.29=2,443.5m? Error in initial summary. Corrected precise calc:
t=2hg=26009.8=265.306122≈16.289 st=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2600}{9.8}}=\sqrt{265.306122}\approx 16.289,\mathrm{s}t=g2h​​=9.82600​​=265.306122​≈16.289s
150×16.289=2,443.35 m150\times 16.289=2,443.35,\mathrm{m}150×16.289=2,443.35m. But similar problems use g=10 for round numbers; with g=9.8 it's ~2.44 km.

Standard forum consensus rounds g=9.8, distance ~2,440 m.

Quick Comparison Table

Parameter| Value| Equation Used 1
---|---|---
Time to ground| 16.3 s| t=2h/gt=\sqrt{2h/g}t=2h/g​
Horizontal distance| 2,440 m| d=vtd=vtd=vt
Vertical velocity at impact| 160 m/s| vy=gtv_y=gtvy​=gt

Real-World Context

In reality, air resistance reduces both time and distance slightly, but this ideal model is standard for physics problems. Pilots in WWII supply drops aimed ~2-3 km ahead for similar speeds/heights.

TL;DR: ~2,440 meters horizontally.

Information gathered from public forums or data available on the internet and portrayed here.