Answer:
v₀₁= 5.525 m / s
Explanation
Freefall Formulas :
The sign of acceleration due to gravity (g) is positive if the object is going down and negative if the object is going up.
vf= v₀+gt
vf²=v₀²+2*g*h
h= v₀t+ (1/2)*g*t²
Where:
h: hight in meters (m)
t : time in seconds (s)
v₀: initial speed in m/s
vf: final speed in m/s
g: acceleration due to gravity in m/s²
Kinematics of the rock from the starting point with vo until it reaches its maximum height:
vf₁= v₀₁-gt₁ :vf₁ =0 to maximum height
0= v₀₁-gt₁
v₀₁ = g*t₁
t₁ =v₀₁ / g Equation (1)
vf₁²= v₀₁²-2*g*h₁ : vf₁ =0 to maximum height
0 = v₀₁²-2*g*h₁
2*g*h₁ = v₀₁²
h₁ = (v₀₁²)/(2g) Equation (2)
Kinematics of the rock when it falls from the maximum height until it touches the floor
h₂= v₀₂t+ (1/2)*g*t₂² v₀₂=vf₁ =0
h₂= 0+ (1/2)*g*t₂²
h₂= (1/2)*g*t₂² Equation (3)
Equation that relates h₁ to h₂
h₂= h₁ + 56.3 , h₁ = (v₀₁²)/(2g)
h₂= (v₀₁²)/(2g) + 56.3 Equation (4)
Equation that relates t₁ to t₂
t₁ + t₂ =4 s
t₂ =4 -t₁
t₂ =4 -(v₀₁/g )
Calculation of v₀₁
We replace equation 4 and equation 5 in equation 3
(v₀₁²)/(2g) + 56.3 = (1/2)*g*(4 -(v₀₁/g ) )²
(v₀₁²)/(2g) + 56.3 = (1/2)*g* (16 - 2*4*(v₀₁/g )+((v₀₁/g )²)
we eliminate (v₀₁²)/(2g) on both sides of the equation
56.3 = (1/2)*g* (16 - 2*4*(v₀₁/g ))
56.3 = 78.4 - 4*v₀₁
4*v₀₁ =78.4-56.3
v₀₁= (78.4-56.3) / ( 4)
v₀₁= 5.525 m / s
