Assume that g = 9.8 m/s², the acceleration due to gravity.
The maximum height is given as h = 0.510 m.
At maximum height, the vertical velocity is zero.
If the initial vertical velocity is v₀ m/s, then
v₀² - 2gh = 0
v₀² = 2gh
= 2*(9.8 m/s²)*(0.510 m) = 9.996 (m/s)²
v₀ = 3.162 m/s
Answer: 3.16 m/s (nearest hundredth)
