A plane is being tracked by radar, and data is taken every second in polar coordinates
θ and r
t (sec) 200 202 204 206 208 210
θ (rad) 0.75 0.72 0.70 0.68 0.67 0.66
r (m) 5120 5370 5560 5800 6030 6240
1. Calculate the velocity of the plane as a function of time, where the velocity V is given by:
V= √r^2 + r(θ)^2.
Please compute the derivatives using the most accurate finite-difference method and comment on the choices you made (why did you choose to use a certain method at any given point).

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

The filament of an incandescent lamp has a temperature of 2000k. calculate the fraction of radiation emitted in the visible light band if the filament is approximated as blackbody

Water in a partially filled large tank is to be supplied to the roof top, which is 8 m above the water level in the tank, through a 2.2-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kpa (gage) in the tank. if the head loss in the piping is 2 m of water, determine the discharge rate of the supply of water to the roof top in liters per second.