Calculate the parametric equations given two points

Question

Jake and Paul start moving on the xy plane at the same time. Jake starts from (-2,5) and heads to (4,-3) on a straight path. Jake gets to his point in 5 seconds.

Paul begins at (-5, 3) and goes directly in a straight path to (5,6).

They cross the y-axis at the same time.

Distance is measured in feet.

1) Calculate the parametric equations for Jake and Paul.

2) How fast is Jake?

3) How fast is Paul?

Include graph.

Answer 1

Parametric Equations

Jake's x = −2 + (6/5) t , y = 5− (8/5) t, t denotes the time and 0≤ t ≤ 5

Paul's x = −5 + 3 t , y = 3− (9/10) t, t denotes the time and 0≤ t ≤ 10/3

They meet on the y-axis at time at time t =5/3

Jake's speed 2m/sec

Paul's speed (3/10)√109