Finding Initial Velocity of a Ball Using Time and Distance

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SUMMARY

The initial velocity of a ball thrown into the air can be calculated using the total flight time and the principles of kinematics. In this discussion, the ball passes a window 0.3 seconds after being released and returns 1.5 seconds later, resulting in a total flight time of 2.1 seconds. By recognizing that the upward and downward motions are symmetrical, one can determine that the time taken to reach maximum height is 1.05 seconds. This time can then be used to calculate the initial velocity using the formula for free fall.

PREREQUISITES
  • Understanding of kinematic equations
  • Knowledge of free fall motion
  • Familiarity with the concept of symmetry in projectile motion
  • Basic algebra for solving equations
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion
  • Learn how to derive initial velocity from time and distance
  • Explore the effects of air resistance on projectile motion
  • Practice problems involving symmetrical motion in physics
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Students studying physics, educators teaching kinematics, and anyone interested in understanding the principles of projectile motion and free fall.

thegreatone09
A ball is thrown up into the air and it passes a certain window 0.3s after being released. It passes the same window on its way back down 1.50s later. What was the intial velocity of the ball?
Any help will be appreciated.
 
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Ask yourself what the total flight time of the ball was.
 
Here's a simple hint I can give: if resistance is ignored, then the upward motion is 'symmetrical' to the downward motion.
 
total time

If you haven't got it by now the total time is 0.3 +1.5 + 0.3 = 2.1 s. Since the velocity is zero at it's maximum height you can divide the time in half to find how long it takes the ball to fall from its maximum height to the ground. Then use that time to calculate distance and then final velocity.
 

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