Question

Micheal and his younger sister Elizabeth are having a race in the backyard. Michael gives his sister a head start and they run for 20 secs. The distance they are along in the race, in feet, is given by; Micheals distance given by the function m(t) and Elizabeth’s distance by the function e(t). Explain your answersA) how do you interpret the fact that m(14)=35? B) if both runners start at t=0, how much of a head start does Michael give his sister?C) does Michael catch up to his sister?D) how far does Michael run during the 20 second race? How far does Elizabeth run?

Answer 1

(A) How do you interpret the fact that m(14) = 35?

Looking at the graph, at the line m(t), we can see a dot. This dot can be traced to the x-axis, where the time (t) is 14 secs. Tracing this to the y-axis, we get 35.

That is why m(14) = 35.

(B) If both runners start at t = 0, how much of a head start does Michael give his sister?

Looking at the graph, you can see the difference between their distance is 25 - 0.

Hence, Michael gave his sister a head start of 25 ft

(C) Does Michael catch up to his sister?

If we remember earlier, the question says that they only ran for 20 secs. Looking at the graph, the line for Michael's race and the sister's race did not meet. If the lines met, then Michael caught up with the sister. Since the lines do not meet up to the 20th second, then, Michael did not catch up with the sister

(D) How far does Michael run during the 20 second race? How far does Elizabeth run?

From the graph, at the 20th second, tracing from Michael's line m(t)

Michael ran 50 ft.

Tracing from Elizabeth's line e(t),

Elizabeth ran 60