Q84 / 180 · KCET 2012 · Mathematics

If a ball is thrown vertically upwards and the height ' $\mathrm{s}$ ' reached in time ' $\mathrm{t}$ ' is given by $s=22 t-11 t^{2}$, then the total distance travelled by the ball is

  • A
    44 units
  • B
    33 units
  • Correct answer
    C
    11 units
  • D
    22 units

Solution

Given, $s=22 t-11 t^{2}$ On differentiating Eq. (i) w.r.t. time (t), we get $$ \frac{d s}{d t}=22-11 \cdot 2 t $$ For maximum, $\frac{\mathrm{ds}}{\mathrm{dt}}$ must be equal to zero. (negative) For $\mathrm{t}=1, \mathrm{~s}$ is maximum. and the maximum value $=22 \times 1-11(1)^{2}$ $$ =22-11=11 $$ Hence, total distance travelled by the ball is 11 units.

Hence, the correct answer is option: 'C'.

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