Question

The US athlete Florence Griffith-Joyner won the 100 m sprint gold medal at Seoul Olympics in 1988, setting a new Olympic record of 10⋅54 s. Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line. Take her mass to be 50 kg. (a) Calculate the kinetic energy of Griffith-Joyner at her full speed. (b) Assuming that the track, wind etc. offered an average resistance of one-tenth of her weight, calculate the work done by the resistance during the run. (c) What power Griffith-Joyner had to exert to maintain uniform speed?

Answer 1

(a)The athlete's K.E is 2251 J at full speed.

(b)The resistance function is -4900 N.

(c)The power to keep the speed uniform is 465 W.

Explanation:

Step 1:

Here's the answer

Given Mass m = 50 kg.

Distance (d) = 100 m

Time (t) = 10.54 sec

Step 2:

Athlete's uniform speed v = d/t

=100/10.54

v = 9.49 m/s.

(a) Athlete's K.E at the  full speed = 1/2 m$v^2$

=1/2 × 50× $(9.49)^2$

=1/2 × 50 × 90.06  

=1/2 × 4503.005  

=2251.5025 ≈ 2251 J  

= 2251 J.

The athlete's K.E is 2251 J at full speed.

(b) Work done by the  resistance :

The athlete's weight = mg

g=9.8 m/s

m = 50 kg

   = 50 × 9.8

   =490 N.

Force of the resistance  

F = mg/10

F = (50 × 9.8) /10

F = 490/10

F = 49 N.

Since she runs at constant speed, there is zero net force in the direction of motion.  

Now the resistance works,

= F ×S

= 49 × (-100 )    { Shows negative sign, counter to force }

= - 4900 J.

Thus the resistance function is -4900 N.

(c)Power to maintain uniform speed With a power of 49 N and a steady speed of 9.49 m/s,

Power = F × v  

P = 49 × 9.49

P = 465 W.

Therefore, the power to keep the speed uniform is 465 W.

Answer 2

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