4. A copper kettle of mass 1 kg contains 0.9 kg of water at 15°C. It takes 12 minutes to rise the temperature to 95°C. If the electric energy is supplied at 220V, calculate the electric current, assuming 10% of heat is wasted. Given specific heat of copper = 420 J kg-K-1 and specific heat of water = 4200 J kg-1 K-1.​

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.

Science and technology are interdependent. advances in one lead to advances in the other. give an example of this phenomenon.

During a medieval siege of a castle, the attacking army uses a trebuchet to hurl heavy stones at the castle walls. if the trebuchet launches the stones with a velocity of at an angle of 50.0°, (a) how long does it take the stone to hit the ground? (b) what is the maximum distance that the trebuchet can be from the castle wall to be in range? (c) how high will the stones go? show all your work.