Question

An astronaut floating freely in space decides to use his flash light as a rocket. He shines a 10 watt light beam in a fixed direction so that he acquires momentum in the opposite direction. If his mass is 80 kg, how long must he need to reach a velocity of 1 m/s
A. 9 s
B. $2.4 \times {10^9}{\text{sec}}$
C. $2.4 \times {10^3}{\text{sec}}$
D. $2.4 \times {10^6}{\text{sec}}$

Answer 1

Hint: The rate of change of an object's direction with respect to a frame of reference is its velocity, which is a function of time. A definition of an object's speed and direction of travel (e.g. 60 km/h to the north) is equal to velocity. In kinematics, the branch of classical mechanics that explains the motion of bodies, velocity is a fundamental concept.

Formula used:
$E = m{c^2}$
E= energy
M = mass of body
C = velocity of light

Complete step-by-step answer:
Linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of an object's mass and velocity in Newtonian mechanics. It's a two-dimensional vector quantity with a magnitude and a direction. The object's momentum is p = mv if m is its mass and v is its velocity (also a vector quantity).
The rate of change of a body's momentum is proportional to the net force acting on it, according to Newton's second law of motion. Momentum varies depending on the frame of reference, but it is a conserved quantity in each inertial frame, meaning that if a closed system is not influenced by external forces, the overall linear momentum remains constant.
Allow t seconds for the astronaut to reach a velocity of 1 m/s.
The energy of photons is then equal to 10 t.
$E = m{c^2}$
 10t = mc
${\text{t}} = \dfrac{{80 \times 1 \times 3 \times {{10}^8}}}{{10}} = 2.4 \times {10^9}{\text{sec}}$

So, the correct answer is “Option C”.

Note: The relationship between mass and energy in a system's rest frame, where the two quantities vary only by a constant and the units of measurement, is known as mass–energy equivalence in physics. The famous formula of physicist Albert Einstein describes the principle: $E = m{c^2}$