A car is moving at high speed along a highway when the driver makes an emergency braking. The wheels become locked (stop rolling), and the resulting skid marks are d = 33 meters long. The coefficient of kinetic friction between tires and road is μ = 0.55 and the acceleration was constant during braking. Write an equation for the speed of the car when its wheels became locked using variables from the problem statement. Use g for acceleration due to gravity.

The intensity, or loudness, of a sound can be measured in decibels (db), according to the equation , where i is the intensity of a given sound and is the threshold of hearing intensity. what is the intensity, in decibels, [i(db)], when ? use a calculator. round to the nearest whole number. 8 9 19 80

Aquantity of gas has a volume of 1.5 m3 and an absolute pressure of 95 kpa. when the gas is compressed to a volume of 0.5 m3, what is the new absolute pressure of the gas? (assume that there’s no change in temperature.)

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.