In the problem, please assume the free-fall acceleration g = 9.80 m/s2 unless a more precise value is given in the problem statement. Ignore air resistance.

A stone is thrown vertically downward from the roof of a building. It passes a window 15.0 m below the roof with a speed of 24.3 m/s. It lands on the ground 4.75 s after it was thrown.

(a) What was the initial velocity of the stone?

(b) How tall is the building?

If building has height H, and stone has initial velocity V,

h(t) = H - 15t - 4.9t^2
h(4.75) = 0 = H - 15(4.75) - 4.9*4.75^2
= H - 181.81

so, H = 181.81m

H-15 = H-15t-4.9t^2
t = .794
v(t) = V - 9.8t
-24.3 = V - 9.8*0.794
V = -16.52m/s

thanks for the assistance, but apparently none of the answers are correct according to my homework checker.

h=(v²-vₒ²)/2•g,

vₒ= sqrt(v²-2•gvh) =
sqrt(24.3²-2•9.8•15) = 17.22 m/s.
H=vₒ•t+g•t²/2 =
17.22•4.75+9.8•4.75²/2 =192.35 m

To find the initial velocity of the stone and the height of the building, we can use the equations of motion for vertically thrown objects.

(a) To find the initial velocity of the stone, we can use the equation of motion:

v = u + gt

where:
v = final velocity (in this case, the speed of the stone passing the window - 24.3 m/s)
u = initial velocity (what we want to find)
g = acceleration due to gravity (9.80 m/s^2)
t = time taken (4.75 s)

Rearranging the equation, we have:

u = v - gt

Substituting the given values, we get:

u = 24.3 m/s - (9.80 m/s^2)(4.75 s)
u = 24.3 m/s - 46.45 m/s
u = -22.15 m/s

So, the initial velocity of the stone is approximately -22.15 m/s (negative because it is thrown vertically downward).

(b) To determine the height of the building, we can use another equation of motion:

s = ut + (1/2)gt^2

where:
s = distance traveled (15.0 m, the distance from the roof to the window)
u = initial velocity (what we found before - -22.15 m/s, negative because it is downward)
t = time taken (4.75 s)
g = acceleration due to gravity (9.80 m/s^2)

Rearranging the equation, we have:

s = ut + (1/2)gt^2

Rearranging the equation again with respect to s, we get:

s = ut + (1/2)gt^2
s - (1/2)gt^2 = ut
s = ut - (1/2)gt^2

Substituting the given values, we get:

15.0 m = (-22.15 m/s)(4.75 s) - (1/2)(9.80 m/s^2)(4.75 s)^2

Solving this equation will give us the height of the building.