Question

(a) A ball is dropped from a height of 30m. After striking the surface it rises to $\frac{2}{3}$ of its height. Again it falls on the surface and this time it covered only $\frac{2}{5}$ of its previous height. It continued for next two times and it only covered half of its previous height. Find the distance covered by the ball.

(b) Which of the following inequalities are correct?

(i) $\frac{-1}{5}<\frac{-3}{5}$

(ii) $\frac{-3}{5}<\frac{-1}{5}$

(iii) $\frac{3}{5}>\frac{1}{5}$

[4 MARKS]

Answer 1

Each part: 2 Marks


(a) After striking to the surface, the height gained by ball is $30m\times \frac{2}{3}=20m$.

Now it attained the height of 20m, height attained by ball after $2^{nd}$ strike is $20\times \frac{2}{5}=8m$.

After $2^{nd}$ strike, height attained by ball is $8\times \frac{1}{2}=4$.

So for $3^{rd}$ strike, it falls from a height of 4m.

Again he attained half of the height of previous so this time it covers 2m.

So total distance covered by ball = 30+ 20+8+4+2 = 64.


(b) (i) $\frac{-1}{5}<\frac{-3}{5}$ is incorrect

The following inequalities are correct:

(ii) $\frac{-3}{5}<\frac{-1}{5}$

(iii) $\frac{3}{5}>\frac{1}{5}$