Question

A hovercraft passes point A moving west with a speed of 15m/seconds. The hovercraft begins to accelerate at a steady rate of 2m/sec² east. How long is it before the hovercraft passes point A moving east and with what speed it will be moving as it does so?

Answer 1

Explanations & Calculations

• This is pretty much the same as the vertical motion under gravity. Apply $\small s = ut+1/2at^2$ with respect to point A taking West to be the positive side.
• When it passes A again the displacement is zero.

$\qquad\qquad \begin{aligned} \leftarrow\\ \small 0&=\small (15\,ms^{-1})t+\frac{1}{2}(-2\,ms^{-2})t^2\\ \small t&=\small 15\,s\quad(t>0) \end{aligned}$

• If it was guessed from the vertical motion under gravity, hovercraft should move at the same speed (15m/s) East as it passes A again.
• To calculate this apply $\small v = u+at$ westward.

$\qquad\qquad \begin{aligned} \small v&=\small 15+(-2\,ms^{-2})(15\,s)\\ &=\small -15\,ms^{-1}\quad(correct: eastwards) \end{aligned}$