A pilot with two passengers on board landed on a 2,100 foot east-west gravel strip having an elevation of 1,800 feet. The temperature is warmer than expected and after computing the density altitude, the pilot determined the takeoff distance over a 50 foot obstacle to be 1,980 feet. The airplane is 75 pounds under gross weight. What would be the best choice?

A. Go for the flight as there is a leeway of 120 feet for takeoff
B. Have the pilot take off by himself and see how the takeoff performance was without the weight of the passengers.
C. Call the tower and see if anyone else has reported climb-out performance problems
D. Postpone the flight and wait for cooler temperatures to recalculate takeoff performance

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.