Question

The motion of a human body through space can be modeled as the motion of a particle at the body's center of mass. The components of the position of an athlete's center of mass from the beginning to the end of a certain jump are described by the following two equations, where t is the time at which the athlete lands after taking off at t = 0.
xf = 0 + (9.6 m/s)(cos 18.5°)t
0.140 m = 0.710 m + 0 + (9.6 m/s)(sin 18.5°)t - (9.80 m/s2)t2
(a) Identify his vector position.
( i + j) m
(b) Identify his vector velocity at the takeoff point.
m/s °
(c) The world longjump record is 8.95 m. How far did the athlete jump in this problem?
(d) Describe the shape of the trajectory of his center of mass.

Answer 1

no answer

Answer 2

. The motion of a human body through space can be
modeled as the motion of a particle at the body’s cen-
ter of mass as we will study in Chapter 9. The compo-
nents of the displacement of an athlete’s center of mass
from the beginning to the end of a certain jump are
described by the equations
xf 5 0 1 (11.2 m/s)(cos 18.5°)t
0.360 m 5 0.840 m 1 111.2 m/s2 1sin 18.582t 2 1
2 19.80 m/s
2 2t
2
where t is in seconds and is the time at which the ath-
lete ends the jump. Identify (a) the athlete’s position
and (b) his vector velocity at the takeoff point. (c) How
far did he jump?