Answer:
4 s
-24.5 m/s
Step-by-step explanation:
y = y₀ + v₀ t + ½ at²
v = at + v₀
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 = 19.6 m
v₀ = 14.7 m/s
g = -9.8 m/s²
Find: t, v
Substitute values into the first equation and find t:
y = y₀ + v₀ t + ½ at²
0 = 19.6 + 14.7 t + ½ (-9.8) t²
0 = 19.6 + 14.7 t − 4.9 t²
0 = t² − 3 t − 4
0 = (t − 4) (t + 1)
t = -1 or 4
Since t must be positive, t = 4 seconds.
Now use the second equation to find v:
v = at + v₀
v = (-9.8) (4) + 14.7
v = -24.5