Question

A stone projected vertically upwards raises 's' feets in 't' seconds where ${}_S=112t-{16t}^2$ then the maximum height it reached is

• A. 195 ft
• B. 194 ft
• C. 196 ft
• D. 216 ft

Answer 1

Answer: (C)

196 ft

$s=112t-16t^2$

for maximum height

$\frac{ds}{dt}=0$

$\frac{d(112t-16t^2)}{dt}=0$

$\frac{d\left(112t\right)}{dt}-\frac{d\left(16t^2\right)}{dt}=0$

$112-16\left(2\right)t^{2-1}=0$

$112-32t=0$

$32t=112$

$t=\frac{112}{32}=\frac{28}{8}=\frac{7}{2}$

$\therefore$ maximum height

$=112\left(\frac{7}{2}\right)-16{\left(\frac{7}{2}\right)}^2$

$=56\times 7-4\times 49$

$=392-196$

$=196ft$