What is the Maximum Height and Flight Time of an Arrow Fired Upward?

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SUMMARY

An arrow fired upward with an initial speed of 38 m/s reaches a maximum height of 73.75 meters. The total time taken for the arrow to return to the ground is 7.76 seconds. At 1.3 seconds, the arrow is at a height of 41.11 meters, and at 3.8 seconds, it is approximately at its maximum height of 73.64 meters. These calculations utilize the equations of motion, specifically x = Vo*t + 0.5*a*t^2 and y = 0.5gt^2.

PREREQUISITES
  • Understanding of kinematic equations
  • Basic knowledge of projectile motion
  • Familiarity with gravitational acceleration (g = 9.81 m/s²)
  • Ability to perform algebraic calculations
NEXT STEPS
  • Study the derivation of kinematic equations for projectile motion
  • Learn about the effects of air resistance on projectile trajectories
  • Explore advanced topics in physics such as energy conservation in projectile motion
  • Practice solving similar problems involving different initial velocities and angles
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Students studying physics, educators teaching kinematics, and anyone interested in understanding the principles of projectile motion.

joel amos
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Homework Statement


An arrow is fired upward with an initial speed of 38 m/s. What is it's maximum height? How long does it take to return to the ground? How high is it at 1.3 seconds? How high at 3.8 seconds?


Homework Equations


x = Vo*t + .5*a*t^2
y = .5gt^2
etc.

The Attempt at a Solution


I got 73.75 m for the maximum height, 7.76 s for the time to return, 41.11 m at 1.3 seconds and 73.64 m at 3.8 seconds (which is basically the maximum height). Am I correct?
 
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