Answer:
The maximum height reached is approximately 44.1 meters
Explanation:
The upward (vertical) velocity of the ball = 29.4 meters per second
The equation of the vertical motion of the ball under gravity, is presented as follows;
v² = u² - 2 × g × s
Where;
v = The final velocity of the ball = 0 at maximum height
u = The initial vertical velocity with which the ball was thrown= 29.4 m/s
g = The acceleration due to gravity ≈ 9.8 m/s²
s = The height reached by the ball = [tex]s_{max}[/tex] at maximum height
∴ 0 = 29.4² - 2 × 9.8 × [tex]s_{max}[/tex]
29.4² = 2 × 9.8 × [tex]s_{max}[/tex] = 19.6·[tex]s_{max}[/tex]
[tex]s_{max}[/tex] = 29.4³/19.6 = 864.36/19.6 = 44.1 meters
[tex]s_{max}[/tex] = The maximum height reached = 44.1 meters.
The maximum height reached by the ball is 43.2 meters.
Using the formula:
v² = u² + 2gH
where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity and H is the height.
At maximum height, v = 0. Given that u = 29.4 m/s, g = -10 m/s (moving upward). Hence:
0² = 29.4² + 2(-10)H
20h = 29.4²
h = 43.2 meters
The maximum height reached by the ball is 43.2 meters.
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