Q. A stone is dropped from the window of a bus moving at 60 km/hr. If the window is 196cm high, what is the distance along the track which the stone moves before striking the ground ?

Jun 15, 2018

Let's get our units consistent.
Acceleration due to gravity: $g = 9.8 \frac{m}{s} ^ 2$
Speed: $60 \frac{\cancel{k m}}{\cancel{h r}} \cdot \frac{1000 m}{1 \cancel{k m}} \cdot \frac{1 \cancel{h r}}{3600 s} = 16.67 \frac{m}{s}$
Distance to fall: $196 \cancel{c m} \cdot \frac{1 m}{100 \cancel{c m}} = 1.96 m$

We need the time to hit the ground, so we need the formula

$y = u \cdot t + \frac{1}{2} \cdot a \cdot {t}^{2}$

$1.96 m = 0 + \frac{1}{2} \cdot 9.8 \frac{m}{s} ^ 2 \cdot {t}^{2}$

${t}^{2} = \frac{2 \cdot 1.96 \cancel{m}}{9.8 \frac{\cancel{m}}{s} ^ 2} = 0.4 {s}^{2}$

$t = 0.632 s$

Now we can calculate the distance down the road it travels in that time. It is

$d = 16.67 \frac{m}{\cancel{s}} \cdot 0.632 \cancel{s} = 10.5 m$

I hope this helps,
Steve