Question

A wide receiver catches a ball and begins to run for the endzone following a path defined by . A defensive player chases the receiver as soon as he starts running following a path defined by . Write parametric equations for the path of each player. a. receiver: defensive: c. receiver: defensive: b. receiver: defensive: d. receiver: defensive:

Answer 1

Receiver path:

x-5 = t(0)

y-50 = -10t

defender path:

x-10 = -0.9t

y-54 =-10.72t

Yes, he will reach the goal line (y = 0) before the defensive player catches him.

Explanation:

Vector equation: (x-x1, y-y1) = t(a1, a2)

Horizontal component : x-x1= ta1

Vertical component: y-y1= ta2

(x-5, y-50) = t(0, -10)

x-5 = t(0)

y-50 =t(-10)

Parametric equation for the receiver path:

x-5 = t(0)

y-50 = -10t

(x - 10, y - 54) = t(-0.9, -10.72)

x - 10 = t(-0.9)

y - 54 = t(-10.72)

Parametric equation for the defender path:

x-10 = -0.9t

y-54 =-10.72t

At the 50yard line, using the receiver parametric equation for vertical component:

y-50 = -10t

At y= 50

50-50 = -10t

0= -10t

t= 0/-10 = 0

At y= 0

0-50 = -10t

t = -50/-10 = 5

Defender at y = 50

y-54 =-10.72t

50-54 =-10.72t

t = -4/-10.72 = 0.37

at y = 0

0-54 =-10.72t

t = -54/-10.72 = 5.04

t of receiver < t of defender

Since time of receiver at y=0 is less than time of defender, he will reach the goal line (y = 0) before the defensive player catches him.