Projectile Motion Challenge Problem

AI Thread Summary
To determine when Mr. Smith should throw the treat for Rosie to catch it mid-air, the vertical and horizontal motions of both Rosie and the treat must be analyzed. Rosie’s jump can be broken down into components, revealing her time of flight and maximum height. The treat's trajectory needs to be calculated based on its launch angle and velocity to find when it will intersect with Rosie’s path. The key is to synchronize the timing of both motions so that they meet at the same point in space. A clear game plan involves calculating the time it takes for Rosie to reach her peak and descend, while simultaneously determining the treat's flight time to ensure they coincide.
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Mr. Smith’s dog Rosie takes a flying leap off his bed. The bed is 1m high, and Rosie leaves with a muzzle velocity of 5 m/s [40° above the horizontal].
Sometime after Rosie leaves the bed, Mr. Smith (who is 5m away from the bed) throws a doggie treat to Rosie from ground level with a muzzle velocity of 7 m/s [20° above the horizontal].
How many seconds does Mr. Smith need to wait after Rosie leaves the bed, to throw the treat such that Rosie catches the treat in mid-air on her way down?



First I tried to figure out final velocity & vertical distance for rosie ...which I got as 0.32s & 0.526m respectively.
But I am really not getting an idea about how to proceed further ...Please help me with this.
 
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Don't figure anything out until you've figured out your gameplan.

What does it take for Rosie to catch the treat on her way down?
 

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