Question

A rocket is fired vertically from the ground with a resultant vertical acceleration of 10 m s^-2. The fuel is finished in 1 min and it continues to move up. What is the maximum height reached?

• A. 42.3 km
• B. 48.4 km
• C. 36.4 km
• D. 25.6 km

Answer 1

Answer: (C)

Height covered in 1 min,
$s_1=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}\times 10\times {\left(60\right)}^2=18000m$
Velocity attained after 1 min,
v = u + at = 0 + 10 × 60 = 600 m $s^{-1}$
After the fuel is finished, u = 600 m ${}^{s-1}$, v = 0
v${}^2-u^2=2g{s}_2$
or$0-{\left(600\right)}^2=2\times \left(-9.8\right)\times s_2$
or$s_2=\frac{{\left(600\right)}^2}{2\times 9.8}=18367.3m$
Maximum height reached = $s_1+s_2$
= 36367.3 m = 36.4 km