Motion problem for constant acceleration of rabbit

[chroncile]

Homework Statement

A rabbit runs past a bush where a wolf is lying in wait. The rabbit is running at 3.0 m/s. The wolf leaps out 0.50 seconds after the rabbit has passed and accelerates at 1.2 m/s² chasing after the rabbit. If the wolf can keep up this acceleration, how long will it take for the wolf to catch the rabbit?

Homework Equations

d = vi * t + 0.5 * a * t^2

The Attempt at a Solution

I got 5.85 s, but the answer is 5.46 s so I did it wrong.

 

[Doc Al]

When did you measure the time from? Hint: Where is the rabbit when the wolf starts chasing?

Show how you got your answer.

 

[chroncile]

t_R = t_w + 0.5 s
d_w = d_r + 1.5 m

Wolf:

v_i = 0
a = 1.2 m/s²

d = v_it + 0.5 at²
d = 0.5(1.2)t²
d = 0.6t²

Rabbit:

v = 3.0 m/s
d = v * t
d = 3.0t

Since t_r = t_w + 0.5 s
d_r = 3.0(t_w + 0.5)
d_r = 3.0t_w + 1.5

Wolf:

Since d_w = d_r + 1.5

0.6t² = 3.0t + 1.5 + 1.5
0.6t² - 3.0t - 3.0

t = 5.85 or -0.85

 

[Doc Al]

t_R = t_w + 0.5 s

This is true.

d_w = d_r + 1.5 m

This is only true at the moment the wolf starts moving. Skip it.

Wolf:

v_i = 0
a = 1.2 m/s²

d = v_it + 0.5 at²
d = 0.5(1.2)t²
d = 0.6t²

Good. This is the wolf's position measured from his starting point.

Rabbit:

v = 3.0 m/s
d = v * t
d = 3.0t

Since t_r = t_w + 0.5 s
d_r = 3.0(t_w + 0.5)
d_r = 3.0t_w + 1.5

Good. This is the rabbit's position measured from the wolf's starting point.

Wolf:

Since d_w = d_r + 1.5

Nah. Just set the two positions equal to solve for when the wolf reaches the rabbit.

 

[chroncile]

Okay, great I got the right answer, but can you please explain to me why it's not + 1.5?

 

[Doc Al]

Okay, great I got the right answer, but can you please explain to me why it's not + 1.5?

Initially the distance between them is 1.5 m. But the wolf catches up to the rabbit, which means they are at the same place. You've already included that head start when you wrote your equations.

The way I would solve it (equivalent to yours of course), measuring everything from the moment and position of the wolf when he starts chasing:

Xr = 3t + 1.5

Xw = 0.6t^2

Just set them equal.