Answer:
7.96 s
Step-by-step explanation:
Given the following :
h = 3t³
After t seconds, that is, t = 2
h = 3(2)³ = 3 × 8 = 24 m
Rate of change, Velocity = dh/dt
dh/dt = 3*3t^(3 - 1) = 3*3t² = 9t²
At t = 2 s ; initial velocity = 9(2)² = 9 × 4 = 36 m/s
From the 3rd equation of motion:
v² = u² + 2gh
Where g = acceleration due to gravity 9.8m/s
upward motion, g = - ve
Displacement = - 24
v² = 36² + 2(-9.8)(-24)
v² = 1296 + 470.4
v² = 1766.4
v = sqrt(1766.4)
= 42.03 m/s
Since final velocity is in downward direction : take it as negative.
Recall, :
Velocity = Displacement / time
Displacement = Velocity × time
Average Velocity = (Initial + final velocity) / 2
Displacement = - 24 m
-24 = [(36 + (-42.03)) /2] × t
-48 = - 6.03t
t = 48 / 6.03
t = 7.96s
