Projectile Motion + Linear Motion = Problem

[ktd]

Here's the problem:

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?

Now, I know I need to use the distance equation for projectiles (ie, the cat) that land at the same elevation as it was fired. But I don't understand this in comparison to the mouse.

Anyone?

 

[Doc Al]

Think this way: First figure out how far the cat jumps (horizontal distance covered) and how long the jump takes. Then ask yourself how far does the mouse move in that time. Jump distance = distance behind mouse at time of jump + distance mouse moves during jump.

 

[stunner5000pt]

Assume the mouse was stationary

Then how fast is the cat with respect to the mouse in terms of HORIZONTAL COMPONENTS ONLY.

Now how much distance will the cat cover in time t

Now look at the cat's vertical components
what is the cat's intial velocity and final velocity,and acceleration
Now find the time the cat will be in teh air given this launch speed

Plug back into the first equation you had and that 's the distance you needed

 

[ktd]

Ok, the velocity of the cat would be (4.0 m/s)cos(30degrees), which = 3.46 m/s

The time equation would be 2((Vi)(sin_theta)/g), correct? If I use that equation, what would the Vi be here? In other words, to find the distance the cat travels, wouldn't I use this equation:

Xcat = (4m/s)cos(30deg.) * (2(Vi)(sin(30deg.))/(g))?

If so, would I use the cat's initial speed for the second half?