Maximum height of baseball, given total flight time.

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SUMMARY

The maximum height reached by a baseball with a total flight time of 7 seconds, ignoring air resistance, is 60.03 meters. The initial upward velocity required to achieve this height is 34.3 m/s. To calculate the maximum height, the equations of constant acceleration are utilized, specifically focusing on displacement, initial velocity, final velocity, time, and acceleration due to gravity (9.8 m/s²). The upward flight lasts for 3.5 seconds before descending back to the ground.

PREREQUISITES
  • Understanding of constant acceleration equations
  • Knowledge of kinematic equations for projectile motion
  • Familiarity with concepts of initial and final velocity
  • Basic grasp of gravitational acceleration (9.8 m/s²)
NEXT STEPS
  • Study the five equations of motion in physics
  • Learn how to derive maximum height in projectile motion problems
  • Explore the concept of time of flight in vertical motion
  • Practice problems involving initial velocity and displacement calculations
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Students studying physics, particularly those focusing on kinematics and projectile motion, as well as educators looking for examples of real-world applications of motion equations.

JP123
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Homework Statement


The question i need to answer is: A baseball has a flight time of 7 seconds. What maximum height did it reach? (ignore air resistance.)


Homework Equations


I need to use equation 1 and equation 5 of the constant acceleration equations.


The Attempt at a Solution


I have figured out the initial upward velocity to be 34.3 seconds and now i don't know where to go from here! The answer for maximum height reached is 60.03m but i don't know how to get to this number. Please help!
 
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Since every list of equations is different, we have no idea which equations are "1" and "5."

I am assuming this problem is for a straight up flight. What is the instantaneous velocity at the top of the path? If the entire flight took 7 seconds, how long did it take to get to the top? Do you know the rate of acceleration? Do you know three of the variables for the flight to the top of the path? (yes)
 


If the upward initial velocity is 34.3 seconds, you might need more than just a tweak to finish this problem.
 


JP123 said:

Homework Statement


The question i need to answer is: A baseball has a flight time of 7 seconds. What maximum height did it reach? (ignore air resistance.)


Homework Equations


I need to use equation 1 and equation 5 of the constant acceleration equations.


The Attempt at a Solution


I have figured out the initial upward velocity to be 34.3 seconds and now i don't know where to go from here! The answer for maximum height reached is 60.03m but i don't know how to get to this number. Please help!

once you have that initial vertical velocity, you can use which ever of the 5 equations that include displacment, since you know the initial vel, the final vel [zero - it is at maximum height] the time [3.5 seconds going up, 3.5 coming back down], and the acceleration [9.8 down]
 

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