Calculation of Maximum Height
A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 130 feet per second. What is the maximum height, in feet, the ball will attain?
When an object is thrown vertically up or down from a certain height disregarding any type of friction with the air or any other obstacle, it is a uniformly accelerated rectilinear motion in which the acceleration coincides with the value of gravity.
On the surface of the Earth, the acceleration of gravity can be considered constant, directed downwards. In this case, the initial speed of the ball is 130 feet per second and the acceleration due to gravity is 32 feet per second squared.
Using the formula for vertical motion: vf² = v₀² - 2 * g * Δy, we can find the maximum height attained by the ball.
Given:
Initial speed (v₀) = 130 ft/s
Initial height (y₀) = 2 ft
Acceleration due to gravity (g) = 32 ft/s²
Calculating the maximum height:
vf² = v₀² - 2 * g * Δy
0 = 130² - 2 * 32 * Δy
0 = 16900 - 64 * Δy
64 * Δy = 16900
Δy = 16900 / 64
Δy = 264.06 ft
Therefore, the maximum height (ymax) attained by the tennis ball is 266.06 feet.
Explanation
When an object is thrown vertically up or down from a certain height H, the acceleration coincides with the value of gravity. In this case, the acceleration due to gravity is considered constant and directed downwards.
To study the vertical launch movement, we consider a reference system with the positive direction pointing up. Using the formula vf² = v₀² - 2 * g * Δy, we can calculate the maximum height of the ball.
At the maximum height, the final speed (vf) is 0. By substituting the given values into the formula, we can find the vertical displacement (Δy) which corresponds to the maximum height attained by the tennis ball.
Therefore, the maximum height of the tennis ball is 266.06 feet.
A force is equal to the mass times acceleration. If we have a force of 5N and a mass of 0.6kg, what is the value of acceleration?
Acceleration (a) = Force / Mass
Acceleration (a) = 5N / 0.6kg
Acceleration (a) = 8.33 m/s²
Therefore, the value of acceleration is 8.33 m/s².