Question

You decide to start training to become a faster sprinter. On day 1, you timed your 100m dash and your final time was 18 seconds. After training for a month, on day 30, your final time was 15.5 seconds. Assume your overall mass of 65kg and your % leg mass (17%) remained constant. (a) Find your average speed for both days of training (b) If you apply 350N of force on the ground in the horizontal direction with every step, determine your stride length if your final velocity at the finish line on day 2 was 7.5 m/s.

Answer 1

For the part a) :-

Avg Speed = (total distance travelled )/ (total time taken )

for day 1 => AVG SPEED = 100/18 => 5.55 m/s.

for day 30 => AVG SPEED = 100/15.5 => 6.45 m/s.

For the part b) :-

It is given that FINAL Velocity = 7.5 m/s , but it doesnt seems to be correct as it is stated that with each step the sprinter provides a horizontal force of 350 N .

So the accelaration (constant) =  Force / (mass of the sprinter) => a = 350/65 = 5.38 m/s² .

So , taking the constant Accelaration a =5.38 m/s² , the AVG final velocity will be

(V_final)² = (V_initial)² + 2as    where s = total displacement , V_f = final velocity , V_i = initial velocity

V_final = 0² + 2*5.38*100 => V_final = 32.80 m/s .

So there is an ambiguity in the given numbers as , considering the constant accelaration V_final > 32.80 m/s

as a sprinter always accelarate ,his accelaration is not constant it is increasing gradually in a race or sprint.

so , in practicality the V_final is surely gonna be > 32.80 m/s.

Moreover

STRIDE LENGTH = The distance between two consecutive steps of same leg .