Asoccer ball is kicked from the ground with an initial speed of 19.3 m/s at an upward angle of 45°. a player 54.7 m away in the direction of the kick starts running to meet the ball at that instant. what must be his average speed if he is to meet the ball just before it hits the ground? (consider up and the direction of the ball's initial motion to be the positive y and x directions.)

Hello there

the answer is

Let the initial position from where the ball is kickedat angle 45 deg, be A. The Horizontal range of the ball (AC) is V2 Sin2θ / g = 38.76 Meters

thank you

thermal energy is the answer

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.