Question

QUESTION 1

Joe intercepts a pass 8 yards into the end zone, 19 yards from the right side of the field as he faces the opposite end of the field (see figure). He starts running diagonally, moving at a rate of 4 yd/s down the field and 2 yd/s across the field. Let x and y be his coordinates on the field.

Write parametric equations for his x- and y-coordinates as functions of time t, in seconds, since he intercepted the ball.

If he keeps going straight at the same velocity, what will be his position when t = 10 s?
Yard Line:
Distance from the right side line:

If he keeps going at the same velocity, at what time will he cross the opponent's 40-yard line, x = 60?

The football field is 53 1/3 yards wide. when he crosses the opponent's 40-yard line, will he still be in bounds?

Diagram can be found blondebeliever.tumblr.[com]/precalc (on my blog) under question 1!

Answer 1

I don't have the diagram. If we call (0,0) the goal line at the edge of the field he's 19 yds from, and +x is downfield, and +y is across the field,

x(t) = -8 + 4t
y(t) = 19 + 2t

x(10) = 32
y(10) = 39

60 = -8 + 4t
t = 17

y(17) = 19 + 34 = 53. He'll be a foot inside the sideline. 1ST DOWN!