A stone is thrown vertically upward from the top of a 30m high building with a velocity of 15m/s. Taking the acceleration of stone as 9.81 m/s2. And taking that as constant, determine a) the velocity v and elevations sy of stone above the ground at any time t b) the maximum altitude reached by the stone c) time when the stone strikes the ground

1. The upward decelerated motion

v=vₒ-gt
At the top v=0
t=vₒ/g = 15/9.8=1.53 s.
h=vₒt-gt²/2.
h= vₒ²/2g=11.5 m.
2. Free fall from the height H+h = 30+11.5 = 41.5 m.
H=gt²/2 =>
t=sqrt(2•H/g) = sqrt(2•41.5/9.8)= 2.91 s.
v=gt =9.8•2.91=28.5 m/s.
Total time =1.53+2.91= 4.44 s.

To solve this problem, we can use the equations of motion to determine the velocity and elevation of the stone at any point in time.

a) To find the velocity (v) and elevation (sy) of the stone above the ground at any time (t), we can use the following equations:

1. Velocity equation: v = u + at
- Where 'v' is the final velocity,
- 'u' is the initial velocity,
- 'a' is the acceleration (in this case, -9.81 m/s^2 because the stone is thrown upwards),
- and 't' is the time.

2. Elevation equation: sy = ut + (1/2)at^2
- Where 'sy' is the displacement or elevation above the ground,
- 'u' is the initial velocity,
- 't' is the time,
- 'a' is the acceleration.

Given:
- Initial velocity (u) = 15 m/s (thrown upwards)
- Acceleration (a) = -9.81 m/s^2 (as the stone is thrown upwards)

b) To find the maximum altitude reached by the stone, we need to find the point where the velocity becomes zero. At this point, the stone will momentarily stop before falling back down. We can use the velocity equation to find the time it takes for the stone to reach this point and then find the elevation using the elevation equation.

c) To find the time when the stone strikes the ground, we need to find the point where the elevation (sy) becomes zero. We can use the elevation equation and set sy = 0 to solve for time (t).

Let's now calculate the results using the given values:

a) Velocity and elevation at any time:
- Plug in the values into the velocity equation:
v = 15 m/s - 9.81 m/s^2 * t

- Plug in the values into the elevation equation:
sy = 15 m/s * t - (1/2) * 9.81 m/s^2 * t^2

b) Maximum altitude reached by the stone:
- To find the time it takes for the stone to reach the maximum altitude, set the velocity to zero:
0 = 15 m/s - 9.81 m/s^2 * t_max
Solve for t_max.

- Once you find t_max, substitute it into the elevation equation to find the maximum altitude, sy_max.

c) Time when the stone strikes the ground:
- Set the elevation (sy) to zero:
0 = 15 m/s * t_ground - (1/2) * 9.81 m/s^2 * t_ground^2
Solve for t_ground.

You can calculate these values using the given equations and the given values to get the specific answers for each part of the question.