Calculating Initial Velocity of a Projectile

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Calculating Initial Velocity of a Projectile - Physics Problem

Here's how to solve this problem:

Understanding the Physics

* Free Fall: The ball's motion is governed by gravity. This means it experiences a constant downward acceleration due to gravity (approximately 9.8 m/s²).

* Symmetry: The time it takes for the ball to go up is equal to the time it takes to fall back down.

Calculations

1. Time to Fall: Since the ball takes 3.0 seconds to go up, it also takes 3.0 seconds to fall back down. The total time in the air is 3.0 s + 3.0 s = 6.0 s.

2. Final Velocity: When the ball hits the ground, its final velocity is the same as its initial velocity (but in the opposite direction). We can use the following kinematic equation to find the final velocity:

* v_f = v_i + at

* where:

* v_f = final velocity (what we're trying to find)

* v_i = initial velocity (also what we're trying to find)

* a = acceleration due to gravity (-9.8 m/s²)

* t = total time in the air (6.0 s)

3. Solving for Initial Velocity:

* Since the final velocity (v_f) and the initial velocity (v_i) have the same magnitude but opposite directions, we can set v_f = -v_i.

* Substitute this into the equation: -v_i = v_i + at

* Simplify: -2v_i = at

* Solve for v_i: v_i = -at / 2

* Plug in the values: v_i = -(-9.8 m/s²)(6.0 s) / 2