Assume the acceleration of the object is a (t) = - 9.8 meters per second per second. (Neglect air resistance.) With what initial velocity must an object be thrown upward (from a height of 3 meters) to reach a maximum height of 460 meters? (Round your answer to one decimal place.) m/sec

Use this kinematics equation to solve for the initial vertical velocity:

v² = v₀² + 2ad

v = final velocity, v₀ = initial velocity, a = acceleration, d = height traveled

Given values:

v = 0m/s (comes to a rest), a = - 9.8m/s², d = 460m - 3m = 457m

Plug in and solve for v₀:

0² = v₀² + 2 (-9.8) (457)

v₀ = 94.6m/s