1. how fast must a truck travel to stay beneath an airplane that is moving
105 km/h at an angle of 25° to the ground?

The truck must travel by 95.16 km/h to stay beneath the airplane

Explanation:

Lets explain how to solve the problem

How fast must a truck travel to stay beneath an airplane that is moving

105 km/h at an angle of 25° to the ground

The truck moves a long the horizontal ground

The airplane moves 105 km/h at an angle 25° to the ground

The truck must moves with velocity equal the horizontal component

of the velocity of the airplane to stay beneath the airplane

The angle between the line represented the velocity of the airplane

and the ground is 25°

→ The horizontal component of the velocity = v cos(25)

→ The velocity of the airplane is 105 km/h

→ The horizontal component = 105 cos(25) = 95.16 km/h

The velocity of the truck = the horizontal component of the airplane

The truck must travel by 95.16 km/h to stay beneath the airplane

a. are

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.