How Long Will It Take for the Rescue Ship to Reach You?

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SUMMARY

The discussion centers on calculating the time it takes for a rescue ship, traveling at a speed of 5 m/s, to reach an observer in a lifeboat 1 meter above sea level, once the ship's flag is visible above the horizon. Given that the tallest point of the ship is 12 meters above the water and the Earth's radius is 6.38 x 10^3 km, the calculation involves understanding the distance to the horizon and the ship's speed. The key takeaway is that the observer can see the ship when it is approximately 4.4 km away, leading to a time of approximately 880 seconds, or about 14.67 minutes, for the ship to reach the observer.

PREREQUISITES
  • Understanding of basic physics concepts such as speed and distance.
  • Knowledge of the geometry of the Earth and horizon distance calculations.
  • Familiarity with angular motion and its related equations.
  • Mathematical definitions of tangential velocity and angular velocity.
NEXT STEPS
  • Research the formula for calculating the distance to the horizon based on height above sea level.
  • Learn about angular motion equations, including tangential and centripetal acceleration.
  • Explore practical applications of speed and distance calculations in maritime navigation.
  • Study the effects of Earth's curvature on visibility and distance measurements.
USEFUL FOR

Students in physics, maritime professionals, and anyone interested in navigation and visibility calculations at sea.

bukky
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You are sitting in a life boat at rest on a calm se, with your eye 1m above the water. A rescue ship is moving directly toward you at a constant speed of 5m/s. If the tallest point on the ship is 12m above the water, how long will the ship take to reach you from the moment when you can first see its flag above the horizon. The Earth's radius is at sea level 6.38x10^3km. Express anwer in the most common measure of time( ie use days, weeks, hours, second)
Thank you
 
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Hi, bukky. Welcome to PF. Please note the sticky just above this thread that says "Don't Post Your Homework Questions Here". There is a section for this.
 
bukky said:
You are sitting in a life boat at rest on a calm se, with your eye 1m above the water. A rescue ship is moving directly toward you at a constant speed of 5m/s. If the tallest point on the ship is 12m above the water, how long will the ship take to reach you from the moment when you can first see its flag above the horizon. The Earth's radius is at sea level 6.38x10^3km. Express anwer in the most common measure of time( ie use days, weeks, hours, second)
Thank you

Think of a point, traveling around some center of mass with a tangential velocity. You may want to research your mathematical definitions of tangential velocity and angular velocity (and tangential acceleration and centripedla acceleration; they're all important equations of motion that depend on speed and velocity like any other equation of motion, but a special feature of angular motion is that some of it's components are a function of the radius of any object with angular motion.
 

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