Along jumper can jump a distance of 7.4 m when he takes off at an angle of 45° with respect to the horizontal. assuming he can jump with the same initial speed at all angles, how much distance does he lose (in m) by taking off at 429?

0.02 m

Explanation:

R₁ = initial distance jumped by jumper = 7.4 m

R₂ = final distance jumped by jumper = ?

θ₁ = initial angle of jump = 45°

θ₂ = final angle of jump = 42.9°

= speed at which jumper jumps at all time

initial distance jumped is given as

final distance jumped is given as

Dividing final distance by initial distance

distance lost is given as

d =

d = 7.4 - 7.38

d = 0.02 m

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).

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.