A projectile fired from ground level is to reach a maximum height of 1600 feet. What is its initial velocity?
To find the initial velocity of the projectile, we can use the kinematic equation for the maximum height of a projectile:
H = (v^2 * sin^2(theta)) / (2 * g)
where:
H = maximum height (1600 feet)
v = initial velocity
theta = launch angle (assuming 45 degrees for simplicity)
g = acceleration due to gravity (32.2 feet/second^2)
Rearranging the equation, we have:
v^2 = (2 * g * H) / sin^2(theta)
Substituting the given values:
v^2 = (2 * 32.2 * 1600) / sin^2(45)
v^2 = 103040 / (0.5)
v^2 = 206080
v = sqrt(206080)
v ≈ 453.7 feet/second
Therefore, the initial velocity of the projectile is approximately 453.7 feet/second.