The Sun-Earth separation is $1.5 \times 10^{11}\,\text{m}$. State this distance in $\text{Gm}$.
The distance from the centre of the Earth to a satellite above the equator is $42.3\,\text{Mm}$. The radius of the Earth is $6380\,\text{km}$. A microwave signal is sent from a point on the Earth directly below the satellite. Calculate the time taken for the microwave signal to travel to the satellite and back.
The speed $v$ of a sound wave through a gas with density $\rho$ and pressure $P$ is given by $v = \sqrt{\frac{CP}{\rho}}$ where $C$ is a constant. Show that $C$ has no unit.
Underline every scalar quantity in the list below: acceleration, energy, momentum, power, weight.
A boat crosses a river whose water is flowing at $1.8\,\text{m s}^{-1}$. The velocity vectors for the boat and the river water are drawn to scale in Fig.~1.1. When in still water, the boat’s speed is $3.0\,\text{m s}^{-1}$. The boat is heading at an angle of $60^{\circ}$ to the river bank.
On Fig.~1.1, draw a vector triangle or a scale diagram to show the resultant velocity of the boat.
Determine the magnitude of the boat’s resultant velocity.