a pine cone fall straights down from a pine tree growing on a 20o slope. the pine cone hits the ground with a speed of 10m/s. what is the component of the pine cone’s impact velocity parallel and perpendicular to the ground?
The pine cone’s impact velocity components are:
- Parallel to the ground (down the slope): 3.4textm/s3.4\\text{m/s}3.4textm/s
- Perpendicular to the ground: 9.4textm/s9.4\\text{m/s}9.4textm/s
How to think about it (mini‑explanation)
The pine cone is falling straight down (vertically), but the ground is
tilted at 20∘20^\circ 20∘. That means its 10 m/s impact speed makes an angle
of 20∘20^\circ 20∘ with the line perpendicular to the slope.
So you decompose the 10 m/s into:
- Component parallel to the ground:
v∥=10sin20∘≈3.4textm/sv_{\parallel}=10\sin 20^\circ \approx 3.4\\text{m/s}v∥=10sin20∘≈3.4textm/s
- Component perpendicular to the ground:
v⊥=10cos20∘≈9.4textm/sv_{\perp}=10\cos 20^\circ \approx 9.4\\text{m/s}v⊥=10cos20∘≈9.4textm/s
These match the standard worked solutions to this classic textbook-style problem.
TL;DR:
Parallel to ground ≈ 3.4textm/s3.4\\text{m/s}3.4textm/s, perpendicular to
ground ≈ 9.4textm/s9.4\\text{m/s}9.4textm/s.
Information gathered from public forums or data available on the internet and portrayed here.
