Answer: It takes 2.85 seconds.
Explanation: according to the question, the kinematics equation for vertical motion is
y₀ is the initial postion and equals 0 because it is fired at ground level;
v₀ is the initial speed and eqauls 14m/s;
g is gravity and it is 9.8m/s²;
y(t) is the final position and equals 0 because it is when the pumpkin hits the ground;
Rewriting the equation, we have:
0 + 14t - = 0
14t - 4.9t² = 0
t(14 - 4.9t) = 0
For this equation to be zero,
t = 0 or
14 - 4.9t = 0
- 4.9t = - 14
t =
t = 2.86
It takes 2.86 seconds for the pumpkin to hit the ground.