Question

a ball was thrown vertically upward from the ground and reaches a height of 50 meters. a) with what speed was it thrown?
b) how long will it remain in the air?

Answer 1

since h(t) = vt - 4.9t^2, the vertex is at t = v/9.8

so,

v(v/9.8) - 4.9(v/9.8)^2 = 50
v = 31.305 m/s

Now you can find how long it was in the air. Namely, twice as long as it took to reach its max height.