A bike, assimilated to a geometry point, moves an inclined plane making an angle a with the horizontal to jump from point A situated at Im from the ground (OA = Im), with a speed Vo = 87+6j. Determine as a function of Vo, a and g in the reference (xoy): 1.1. The parametric equation of motion. 1.2. The equation of the trajectory and specify its form 2) Prove that Vo=10m/s and a=37°. 3) Determine the maximum altitude. 4) Determine the maximum range. 5) The ceiling of a car is placed in the plan of jump of the bike at the point "C" with a distance 7m (OH=7m) from the launching point and altitude 1,5m from the ground (HC= 1.5m). Can he make the jump without touching the ceiling of the car and fall at risk? 6) Determine the magnitude and the direction of the speed at point "D" when the bike touches the ground? 7) Determine the angles of launching a and az where the range is 9m, knowing that Vo remains the same Ve 10m/s.

the closer the planet is to the sun, the larger the gravity

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.