A pumpkin is thrown upwards at a speed of 27.5 m/s and from a height of 2 m above the ground. How long before it hits the ground and smashes?

Not sure where to begin with this.

2 answers

h = Hi + Vi t - 4.9 t^2
0 = 2 + 27.5 t -4.9 t^2
or
4.9 t^2 -27.5 t - 2 = 0

solve quadratic for t, use the positive answer (any negative root was on the way up before you threw it :)
V^2 = Vo^2 + 2g*h.
0 = 27.5^2 - 19.8h
h = 38.6m. above launching point.

ho + h = 2 + 38.6 = 40.6m above gnd.

V = Vo + g*Tr.
0 = 27.5 - 9.8Tr
Tr = 2.81s. = Rise time.

0.5g*Tf^2 = 40.6.
Tf(fall time) = ?.

Tr+Tf = Time to reach gnd.