# Projectile motion (part 7) | Summary and Q&A

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November 2, 2007
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Projectile motion (part 7)

## TL;DR

This video explains how to calculate the height a ball reaches when thrown vertically, using equations of motion.

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### Q: How do you calculate the initial velocity of a thrown ball?

The initial velocity can be calculated using the equation v = -gt/2, where g is the acceleration due to gravity and t is the time. For example, if the time is 3 seconds, the initial velocity would be -1.5g m/s.

### Q: What is the formula for calculating the height a ball reaches when thrown vertically?

The height can be calculated using the equation h = -gt^2/8, or alternatively, h = -g/2 * (t/2)^2. For instance, if the time is 4 seconds, the height would be -2g m.

### Q: Can the same equations be used for a dropped ball?

Yes, the equations can be used for a dropped ball as well. If the ball is dropped from a height h, we can use the equation -h = -g/2 * (t/2)^2 to calculate the time it takes for the ball to fall.

### Q: How do speed and velocity differ in this context?

Speed represents the magnitude of the velocity, while velocity also includes the direction. In the video, the average velocity over the entire time period is 0 because the ball starts and ends at the same place, despite having varying speeds during its trajectory.

## Summary & Key Takeaways

• The initial velocity of a thrown ball can be calculated using the equation v = -gt/2, where g is the acceleration due to gravity and t is the time.

• The height the ball reaches can be found using the equation h = -gt^2/8, or alternatively, h = -g/2 * (t/2)^2.

• The same equations can be used to calculate the time it takes for a dropped ball to fall from a given height.