Projectile Motion Challenge Problem

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SUMMARY

The Projectile Motion Challenge Problem involves calculating the timing for Mr. Smith to throw a treat to his dog Rosie, who jumps off a 1m high bed with an initial velocity of 5 m/s at a 40° angle. Rosie reaches a vertical distance of 0.526m after 0.32 seconds. To ensure Rosie catches the treat thrown from 5m away at a velocity of 7 m/s at a 20° angle, Mr. Smith must wait a specific duration after Rosie leaves the bed. The key to solving this problem lies in synchronizing the projectile motion of both Rosie and the treat.

PREREQUISITES
  • Understanding of projectile motion principles
  • Knowledge of kinematic equations
  • Familiarity with trigonometric functions for angle calculations
  • Ability to calculate time of flight for projectiles
NEXT STEPS
  • Study the kinematic equations for projectile motion
  • Learn how to calculate the time of flight for different angles
  • Explore the concept of relative motion in projectile problems
  • Practice solving similar projectile motion problems with varying parameters
USEFUL FOR

Students in physics, educators teaching projectile motion, and anyone interested in solving real-world applications of kinematics.

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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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