Math Problem Statement

Solve for initial velocity

Solve for initial velocity

Solution

To solve for the initial velocity v0v_0, we can use the formula provided in the image:

v0=g(average hang time)2v_0 = \frac{g \cdot \text{(average hang time)}}{2}

where:

  • g=9.8m/s2g = 9.8 \, \text{m/s}^2 (acceleration due to gravity),
  • Average hang time is given as 1.39s1.39 \, \text{s}.

Substitute the values:

v0=9.8m/s2×1.39s2v_0 = \frac{9.8 \, \text{m/s}^2 \times 1.39 \, \text{s}}{2}

Now, calculating:

v0=9.8×1.392v_0 = \frac{9.8 \times 1.39}{2} v0=13.6222v_0 = \frac{13.622}{2} v0=6.811m/sv_0 = 6.811 \, \text{m/s}

Answer:

The initial velocity v0v_0 is approximately 6.81m/s6.81 \, \text{m/s}.

Would you like further explanation on any part of this solution?

Related Questions:

  1. How does the angle θ\theta affect the initial velocity calculation if it was included?
  2. What would the initial velocity be if the hang time were doubled?
  3. How does gravity influence the hang time in a projectile motion scenario?
  4. What formula would we use if only the maximum height reached was given?
  5. How would air resistance impact the initial velocity calculation?

Tip:

In projectile motion, always break down motion into vertical and horizontal components to simplify calculations, especially when initial velocity and angles are involved.

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Kinematics

Formulas

T = (2 * v_0 * sin(θ)) / g
v_0 = (g * average hang time) / 2

Theorems

Equations of motion under constant acceleration

Suitable Grade Level

Grades 10-12