Q88 / 150 · MHT CET 2026 (16 April Shift 1) · Mathematics
A ball is thrown in the air. Its height at any time $t$ is given by $h = 3 + 14t - 5t^2$, then the maximum height it can reach
- A$12.9$
- Correct answerB$12.8$
- C$12.7$
- D$12.6$
Solution
Given $h = 3 + 14t - 5t^2$
Differentiating with respect to $t$:
$\dfrac{dh}{dt} = 14 - 10t$
For maximum height, $\dfrac{dh}{dt} = 0$:
$14 - 10t = 0 \Rightarrow t = 1.4$
Substituting $t = 1.4$ in the equation for $h$:
$h_{max} = 3 + 14(1.4) - 5(1.4)^2$
$h_{max} = 3 + 19.6 - 5(1.96)$
$h_{max} = 22.6 - 9.8 = 12.8$
Answer: $12.8$
Differentiating with respect to $t$:
$\dfrac{dh}{dt} = 14 - 10t$
For maximum height, $\dfrac{dh}{dt} = 0$:
$14 - 10t = 0 \Rightarrow t = 1.4$
Substituting $t = 1.4$ in the equation for $h$:
$h_{max} = 3 + 14(1.4) - 5(1.4)^2$
$h_{max} = 3 + 19.6 - 5(1.96)$
$h_{max} = 22.6 - 9.8 = 12.8$
Answer: $12.8$
Hence, the correct answer is option: 'B'.