In a science fiction movie, a lone astronaut with a mass of 75 kg is stranded outside their spaceship with a thruster pack that is not working. they are stationary relative to their ship. in order to get themselves moving they throw a 2.3 kg wrench at 15 m/s in the opposite direction of the ship. a. draw before and after pictures for the astronaut and the wrench labeling masses and velocities. b. what is the speed of the astronaut after they throw the wrench? c. if it takes them 0.12s to stop when they run into the ship, what is the impulse, average force and average acceleration they experience?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

You can decrease the resistance of a length of wire by

Using proper grammar, spelling, and punctuation, write at least one 5 sentence paragraph describing 3 ways we use the elements of the electromagnetic spectrum (ems) in our everyday lives.