1. On a hot summer day in the state of Washington while kayaking, I saw several swimmers jump from a railroad bridge into the Snohomish River below. The swimmers stepped off the bridge, and they hit the water 1.59 s later. How high was the bridge? 2. How fast were the swimmers moving when they hit the water? 3. What would the swimmer's drop time be if the bridge were 2.5 times as high?

1) Height of bridge = 12.4 m

2) Velocity when the swimmers hit the water = 15.58 m/s

3) Time of flight if the bridge was 2.5 times as high = 2.52 s

Explanation:

Using the equations of motion,

g = 9.8 m/s², y = H = ? t = 1.59 s

Initial velocity, u = 0 m/s,

final velocity, v = ?

Total Time of fall, t = 1.59

1) y = ut + gt²/2

y = 0 + 9.8(1.59)²/2

y = 12.4 m

2) v = u + gt

v = 0 + (9.8 × 1.59)

v = 15.58 m/s

3) y = ut + gt²/2

y = 2.5 × 12.4 = 31 m

u = 0 m/s

g = 9.8 m/s²

31 = 0 + 9.8t²/2

4.9t² = 31

t² = 31/4.9

t = 2.52 s

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.

490 n

f=125n a=2.5m/s2