Question

An 65 kg Olympic runner leaps over a hurdle. The acceleration of gravity is 9.81 m/s 2 . If the runner’s initial vertical speed is 2.9 m/s, how much will the runner’s center of mass be raised during the jump? Answer in units of m.

Answer 1

Explanation:

think of it this way

the mass is going up at 2.7 m/s and during that time is being slowed down at a rate of 9.81 m/s^2 by gravity

eventually the vertical velocity slows to zero (and then he starts down)

how long does it take for the 2.7 to become 0 with 9.81 decelleration

the equation looks like this

v=vo+at

with vo being the initial velocity, we are looking for the "t" where the "v" equal 0, so

0=2.7 m/s + (-9.8 m/s^2) t

-2.7 m/s =-9.8 m/s^2 t

-2.7/-9.8 s=t

.276 s=t

so, it takes a little over 1/4 a second for the jumper to hit his height

how high is he at that time (or at least, how much has his center of mass moved)

the equation is

d=do+vo t + 1/2 a t^2

we'll let do be zero, ground level or more correctly initial center of mass level

d= 2.7(.276) m +.5(-9.8)(.276^2) m

d= .371 m

or a little over a foot

I may have made an arithmetic error, you should check it

If I did it right he won't clear a very high hurdle unless his original center of mass was pretty high, but these hurdlers are often long-legged

Answer 2

Answer:

The vertical height in which the runner’s center of mass is raised during the jump is 0.43 m.

Explanation:

The vertical height reached by the runner is calculated by applying the third kinematic equation as shown below.

Step 1: Mathematically, the formula is given as;

v² = u² - 2gh

Step 2: where;

v is the final velocity of the runner at the maximum height

u is the initial velocity of the runner

g is acceleration due to gravity

h is the height reached by the runner

at maximum height, the final velocity, v = 0

Step 3: The vertical height reached by the runner is calculated as;

0 =  u² - 2gh

2gh = u²

h = u² / 2g

h = ( 2.9² ) / ( 2 x 9.8 )

h = 0.43 m

Hence, The vertical height in which the runner’s center of mass is raised during the jump is 0.43 m.

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