Answer:
3.9 seconds
Explanation:
Use constant acceleration equation:
y = y₀ + v₀ t + ½ at²
where y is the final position,
y₀ is the initial position,
v₀ is the initial velocity,
a is the acceleration,
and t is time.
Given:
y = 0 m
y₀ = 15 m
v₀ = 15 m/s
a = -9.8 m/s²
Substituting values:
0 = 15 + 15t + ½ (-9.8) t²
0 = 15 + 15t − 4.9t²
0 = 4.9t² − 15t − 15
Solve with quadratic formula:
t = [ -b ± √(b² − 4ac) ] / 2a
t = [ 15 ± √((-15)² − 4(4.9)(-15)) ] / 2(4.9)
t = [ 15 ± √(225 + 294) ] / 9.8
t = (15 ± √519) / 9.8
t = -0.79 or 3.9
It takes 3.9 seconds for the stone to reach the bottom of the well.
The negative answer is the time it takes the stone to travel from the bottom of the well up to the top of the well.
