Question

Type the correct answer in the box. what’s the velocity of the rocket? use . a rocket with a mass of 10,000 kilograms is propelled upward with 8,000,000 joules of kinetic energy. the velocity of the rocket is meters/second.

Answer 1

$\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}}$

11.1m/s

Explanation:

• To find

The velocity of rocket (m/s)

• Given

Mass (m) = 10,000kg

Kinetic energy (K.E.) = 8,000,000J

velocity v = ?km/h

• Solution

The kinetic energy of the body is caused due to motion of the body. It can never be in negative. And it is directly proportional to the mass of the body and the square of the velocity the body. It is a scalar quantity

So

$\bold {K.E. = \frac{1}{2} m {v}^{2} }$

So the expression for velocity will be

$\sf \large v = \sqrt{ \frac{2K.E.}{m} }$

Now substituting the required values

$\sf \longrightarrow v = \sqrt{ \frac{2 \times 800{ \cancel{0000}}}{ \cancel{10000}} } \\ \\ \sf \longrightarrow v = \sqrt{2 \times 800 } \\ \\ \sf \longrightarrow v = \sqrt{1600} \\ \\ \blue {\boxed {\longrightarrow 40 \: km/h}}$

While looking upon the question the answer should be in m/s

So we are converting km/h into m/s

$\sf while \: 1km/h = \frac{1000}{3600} m/s \\ \sf so \: 1km/h = \frac{5}{18} m/s$

$\sf 40km/h = \frac{5}{18} \times 40m/s \\ \sf = \frac{200}{18} m/s \\ \green{ \boxed {\tt = 11.1m /s}}$