Displacement and Height Calculations with Velocity

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SUMMARY

The discussion focuses on calculating displacement and height based on projectile motion principles. Given a horizontal muzzle velocity of 387 m/s and a distance of 188 m, the bullet was in the air for approximately 0.485 seconds. The height from which the bullet was fired can be calculated using the formula for free fall, resulting in a height of approximately 1.16 meters. Additionally, to hit the same target with an arrow shot at 32.6 m/s, the required height is approximately 0.5 meters.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Basic knowledge of free fall calculations
  • Ability to convert units (meters to feet)
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  • Study kinematic equations for projectile motion
  • Learn about free fall and gravitational acceleration
  • Explore the effects of initial velocity on projectile trajectories
  • Research unit conversion techniques for physics calculations
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1. Homework Statement [/b]

assume g = 9.81 m/s2, and friction can be ignored.

A gun is fired horizontally at a target lying on the ground 188 m away, and the bullet hits the center of the target. The muzzle velocity of the gun (the speed with which it fires bullets) is 387 m/s.

a) How long was the bullet in the air?
in seconds

b) How high was the gun above the ground when it was fired?
in meters

c) Suppose an arrow can be shot out of a bow at 32.6 m/s. How high above the ground would you have to fire the arrow horizontally to hit the same target over the same distance?
in meters

NOTE: Think about how high this is in feet.
 
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