Two astronauts are at rest in outer space, one 20.0 m from the Space Shuttle and the other 40.0

step 1 This question, we have to calculate the time taken by her to reach the space shuttle. So we have

Two astronauts are at rest in outer space, one 20.0 m from...

Two astronauts are at rest in outer space, one $20.0 \mathrm{~m}$ from the Space Shuttle and the other $40.0 \mathrm{~m}$ from the shuttle. Using a $100.0-\mathrm{W}$ laser, the astronaut located $40.0 \mathrm{~m}$ away from the shuttle decides to propel the other astronaut toward the Space Shuttle. He focuses the laser on a piece of totally reflecting fabric on her space suit. If her total mass with equipment is $100.0 \mathrm{~kg},$ how long will it take her to reach the Space Shuttle?

Key Concepts

Newton's Second Law of Motion

Newton's second law, which states that force equals mass times acceleration (F = ma), connects the force resulting from radiation pressure to the acceleration of an object. This law is fundamental in calculating motion when a constant force is applied, such as in laser propulsion.

Radiation Pressure

Radiation pressure is the phenomenon whereby electromagnetic radiation exerts a force on surfaces when it is absorbed or reflected. This concept is essential in understanding how light, including laser beams, can induce a measurable force on objects, even in the vacuum of space.

Photon Momentum Transfer

Photons, despite having no rest mass, carry momentum. When a photon reflects off a surface, especially one that is perfectly reflective, it transfers momentum to that surface. This momentum transfer is the basis for generating forces using light in propulsion applications.

Force from Electromagnetic Radiation

The force generated by electromagnetic radiation, such as a laser beam, is determined by the power of the radiation and the nature of its interaction with material surfaces. In cases of reflection, the force is typically augmented, because the change in momentum is effectively doubled compared to absorption.

Kinematics with Constant Acceleration

Once a constant acceleration is determined from the applied force (using Newton's second law), kinematic equations can be used to compute the time taken or distance traveled by an object. These equations are crucial for predicting the motion of objects under a uniform force, such as that provided by a continuous laser beam.

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