Physics Problem dimensional dynamics?

Question

A cat is chasing a mouse. The mouse runs in a straight line at a speed of 1.5 m/s.
If the cat leaps off the floor at a 30 degree angle and a speed of 4.0 m/s, at what distance behind the mouse should the cat leap in order to land on the poor mouse?

Answer 1

Hmm, like this question....

Let's start with the cat. If it jumps at a 30 degree angle, and has a speed of 4 m/s, then let's calculate the components

vX = 4 cos 30 = 3.46 m/s
vY = 4 sin 30 = 2.00 m/s

The time for the cat to reach max height is:
t = (vF - vI)/g
= (0 - 2.0)/-9.81
= 0.204 s

Doubling this to get total time in flight = 0.408 s

Now let's get the range (Horiz distance) for the cat
d = v * t
= 3.46 * 0.408
= 1.41 meters

Now let's turn to the mouse. In the time of 0.408 seconds, it will travel a distance of:
d = v * t
= 1.5 * 0.408
= 0.612 meters

So let's subtract this distance from the cat's range in flight
1.41 - 0.612 = 0.798 meters

Leaving the answer with 2 significant digits = 0.80 meters

Answer 2

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Answer 3

.802 m