Arianna kicks a soccer ball off the ground and in the air with an initial velocity of 42 feet per second. Approximately what maximum height does the soccer ball reach?
To determine the maximum height reached by the soccer ball, we need to use the principles of projectile motion. In this case, we know the initial velocity of the ball is 42 feet per second.
The maximum height can be found using the following formula:
𝐻 = (𝑣₀²sin²𝜃) / (2𝑔)
where:
- H is the maximum height
- v₀ is the initial velocity
- θ is the launch angle (in this case, we assume it is launched vertically, so sin²θ = 1)
- g is the acceleration due to gravity (approximately 32.2 ft/s²)
Since the ball is launched vertically, the launch angle is 90 degrees, and sin²90° = 1.
Plugging in the values, the formula becomes:
𝐻 = (42² * 1) / (2 * 32.2)
Now, let's simplify and calculate the result:
𝐻 = 1764 / 64.4
𝐻 ≈ 27.34 feet
Therefore, the soccer ball reaches a maximum height of approximately 27.34 feet.
To find the maximum height the soccer ball reaches, we need to make use of the following kinematic equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity (0 feet per second at maximum height),
- u is the initial velocity (42 feet per second),
- a is the acceleration due to gravity (-32 feet per second squared), and
- s is the displacement (the height we're trying to find).
Rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
Now, let's substitute the values into the equation:
s = (0^2 - 42^2) / (2 * -32)
s = (-1764) / (-64)
s ≈ 27.56 feet
Therefore, the approximate maximum height the soccer ball reaches is 27.56 feet.