Question

5. A stone is dropped from the window of a bus
moving at 60 kmh. If the window is 1.96 m high,
find the distance along the track, which the stone
moves before striking the ground. (Ans. 10.5)​

Answer 1

Let's get our units consistent.

Acceleration due to gravity:

$g</p><p>=</p><p>9.8</p><p>m</p><p>s</p><p>2$

$Speed: </p><p>60</p><p>k</p><p>m</p><p> \: h</p><p>r</p><p>⋅</p><p>1000</p><p>m \: </p><p>1</p><p>k</p><p>m</p><p>⋅</p><p>1 \: </p><p>h</p><p>r \: </p><p>3600</p><p>s</p><p>=</p><p>16.67</p><p>m</p><p>s</p><p>$

$Distance \: to \: fall: </p><p>196</p><p>c</p><p>m</p><p>⋅</p><p>1</p><p>m</p><p>100</p><p>c</p><p>m</p><p>=</p><p>1.96</p><p>m$

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

$y</p><p>=</p><p>u</p><p>⋅</p><p>t</p><p>+</p><p>1</p><p>2</p><p>⋅</p><p>a</p><p>⋅</p><p>t</p><p> ^{2}$

$1.96</p><p>m</p><p>=</p><p>0</p><p>+</p><p>1</p><p>2</p><p>⋅</p><p>9.8</p><p>m</p><p>s</p><p>2</p><p>⋅</p><p>t</p><p> ^{2}$

$t {}^{2} </p><p>=</p><p>2</p><p>⋅</p><p>1.96</p><p>m</p><p>9.8</p><p>m</p><p>s</p><p>2 \\ </p><p>=</p><p></p><p></p><p></p><p> </p><p></p><p>t</p><p>=</p><p>0.632</p><p>s$

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

$d</p><p>=</p><p>16.67</p><p>m</p><p>s</p><p>⋅</p><p>0.632</p><p>s</p><p>=</p><p>10.5</p><p>m$

I hope this helps,