Careful measurements have been made of Olympic sprinters in the100-meter dash. A quite realistic model is that the sprinter'svelocity is given by
v_x = a{1 - e^{ - bt} })
Sprinter Carl Lewis's run at the 1987 World Championships ismodeled with a = 11.81 m/s and b = 0.6887{ s}^{ - 1}.
a)What was his time at t=0s.
b)What was his time at t=2.35s
c)What was his time at t=4.35s
d)Find an expression for the distance traveled at time t.
Your expression from part D is a transcendental equation, meaningthat you can't solve it for t. However, it's not hard to use trialand error to find the time needed to travel a specific distance. Tothe nearest 0.01 {\rm{ s}}, find the time Lewis needed to sprint100.0 {\rm m}. His official time was 0.01 {\rm s} more than youranswer, showing that this model is very good, but not perfect
Careful measurements have been made of Olympic sprinters in the100-meter dash. A quite realistic model is that the sprinter'svelocity is given by
v_x = a{1 - e^{ - bt} })
Sprinter Carl Lewis's run at the 1987 World Championships ismodeled with a = 11.81 m/s and b = 0.6887{ s}^{ - 1}.
a)What was his time at t=0s.
b)What was his time at t=2.35s
c)What was his time at t=4.35s
d)Find an expression for the distance traveled at time t.
Your expression from part D is a transcendental equation, meaningthat you can't solve it for t. However, it's not hard to use trialand error to find the time needed to travel a specific distance. Tothe nearest 0.01 {\rm{ s}}, find the time Lewis needed to sprint100.0 {\rm m}. His official time was 0.01 {\rm s} more than youranswer, showing that this model is very good, but not perfect
