Blake\'s higher initial acceleration means that he can outrun a horse over a ver

Question

Blake's higher initial acceleration means that he can outrun a horse over a very short race. Blake accelerates at 8.0 m/s2 for 1.8 s and then runs at a constant speed. A horse accelerates at a more modest 5.0 m/s2 but continues accelerating tor 4.5 s and then continues at a constant speed. Blake and a horse are competing in a 200 m race Blake is given a 100 m head start, so he begins 100 m from the finish line. How much time does Blake take to complete the race? How much time does the horse take? Who wins the race?

Explanation / Answer

for 1.8 sec,

d = u t + a t^2 / 2

d1 = 0 + (6)(1.8^2) /2 = 9.72 m

Speed after that, v = u + a t = 6 x 1.8 = 10.8 m/s

distance remaining = 100-9.71 = 90.28 s

time taken to travel this distance = 90.28/10.8 = 8.36 sec

Total time taken by blake = 1.8 + 8.36 = 10.16 s .............Ans

For Horse:

0 to 4.5s:

d = 0 + (5 x 4.5^2 ) / 2 = 50.625 m

v = 0 + 5 x 4.5 = 22.5 m/s

distance remaing = 200 - 50.625 = 149.375 m

time taken = 149.375 / 22.5 = 6.64 s

total time = 6.64 + 4.5 = 11.14 s .............Ans

time is less for blake hence blake wins.

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