KCET · Maths · Parabola
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
- C 11 units
- D 22 units
Answer & Solution
Correct Answer
(C) 11 units
Step-by-step Solution
Detailed explanation
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.
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.
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