45. In Mostar, Bosnia, the ultimate test of a young man’s courage once was to jump off a 400-year-old bridge (now destroyed) into the River Neretva, 23.0 m below the bridge. (a) How long did the jump last? (b) How fast was the diver traveling upon impact with the water? (c) If the speed of sound in air is 340 m/s, how long after the diver took off did a spectator on the bridge hear the splash?
\(y_f=0m\\y_o=h=23m\\a=-9.8m/s^2\\v_o=0m/s\\t=?\\v_f=?\)
(a) How long did the jump last?
As we already know the distance he has to cover and is falling from rest then we use the equation of position and solve for t;
\(y_f=y_o+v_ot+\frac{at^2}{2}\)
\(0m=23m+\frac{(-9.8m/s^2)t^2}{2}\\ 0=23m-4.9m/s^2*t^2\\ t=\sqrt{\frac{23m}{4.9m/s}}\\\boxed{t=2.16s}\)
\(y_f=0m\\y_o=h=23m\\a=-9.8m/s^2\\v_o=0m/s\\t=?\\v_f=?\)
(a) How long did the jump last?
\(y_f=y_o+v_ot+\frac{at^2}{2}\)
\(0m=23m+\frac{(-9.8m/s^2)t^2}{2}\\ 0=23m-4.9m/s^2*t^2\\ t=\sqrt{\frac{23m}{4.9m/s}}\\\boxed{t=2.16s}\)
(b) How fast was the diver traveling upon impact with the water?
\(v_f=v_o+at=-9.8m/s^2*(2.16s)\\ v_f=-21.16m/s\)
The negative in the velocity stands for the man is falling downwards in the negative axis from the origin y=0.
The negative in the velocity stands for the man is falling downwards in the negative axis from the origin y=0.
(c) If the speed of sound in air is 340 m/s, how long after the diver took off did a spectator on the bridge hear the splash?
As the speed of sound is constant then we just need to apply the easiest equation of position for such motion and solve for t, The time which takes to get to the spectator.
\(x=v*t\\t=\frac{x}{v}=\frac{23m}{340m/s}=0.06s\)
Then the total time is;
\(t_T=2.16s+0.06s=2.22s\)
\(t_T=2.16s+0.06s=2.22s\)
