PHY2601 Assignment 3 Solutions 2026

PHY2601 Assignment 3 Solutions 2026
UNISA

,CHAPTER 10

QUESTION 1 — Velocity relative to an inertial frame

A point on the Earth's equator is rotating with the Earth. An aircraft flies above the
equator at

𝑣 = 1000 km h−1


We need to find its velocity relative to an inertial frame when it flies:

(a) north, (b) west, and (c) east.

Given

Earth's radius:

𝑅 = 6.37 × 106 m

Earth's rotation period:

𝑇 = 24 h = 24(3600)
𝑇 = 86400 s


Aircraft speed:

𝑣 = 1000 km h−1


Convert to m/s:
1000
𝑣 = 1000 ( )
3600
𝑣 = 277.78 m s−1



Calculate the angular velocity of the Earth

The angular velocity is
2𝜋
𝜔=
𝑇


Therefore,
2𝜋
𝜔=
86400
𝜔 = 7.27 × 10−5 rad s−1

, Calculate the velocity due to Earth's rotation

At the equator,

𝑣𝐸 = 𝜔𝑅


Therefore,

𝑣𝐸 = (7.27 × 10−5 )(6.37 × 106 )
𝑣𝐸 ≈ 463.3 m s−1


This velocity is directed eastwards.



(a) Aircraft flies north

The aircraft's velocity is perpendicular to the Earth's rotational velocity.

Therefore, using Pythagoras,

𝑣inertial = √𝑣𝐸2 + 𝑣 2


Substitute:

𝑣inertial = √(463.3)2 + (277.78)2
= √214646.9 + 77160.5
= √291807.4
𝑣inertial ≈ 540.2 m s−1


The direction can also be found:
𝑣𝐸
tan 𝜃 =
𝑣
463.3
tan 𝜃 = = 1.668
277.78
𝜃 ≈ 59.1∘


Thus, the velocity is directed approximately 59.1∘ east of north.

Answer:

𝑣 ≈ 540 m s−1 , 59.1∘ east of north