A stone is thrown upwards from the roof with a velocity 15ms^-1 at an angle 30degree to the horizontal. The height of the building is 40m.calculate the magnitude of the velocity of the stones before it strikes the ground

Vi up = 15 sin 30 = 7.5 m/s initially

u = 15 cos 30 = 13 m/s forever
Hi = 40
then
h = Hi + Vi t - 4.9 t^2
0 = 40 + 7.5 t - 4.9 t^2
or 4.9 t^2 - 7.5 t - 40 = 0
t = [ 7.5 +/- sqrt(56.25 + 784) ] / 9.8
use + root of course
t = 3.72 seconds
then
v = Vi - 9.8 t = 7.5-36.5 = -29 m/s down
so
|v| = sqrt( 169 + 841) = 31.8 m/s

To calculate the magnitude of the velocity of the stone before it strikes the ground, we can break down the motion of the stone into horizontal and vertical components.

We know that the stone is thrown upwards with an initial velocity of 15 m/s at an angle of 30 degrees to the horizontal. The vertical component of the initial velocity can be calculated as follows:

Vertical Component of Initial Velocity = Initial Velocity * sin(angle)

Substituting the values, the vertical component of the initial velocity is given by:

Vertical Component of Initial Velocity = 15 m/s * sin(30 degrees)

Next, using the vertical component of the initial velocity and the height of the building, we can calculate the time it takes for the stone to reach the ground.

The equation that relates time, initial velocity, acceleration, and displacement for motion in a straight line is:

Displacement = (Initial Velocity * time) + (0.5 * acceleration * time^2)

In this case, the displacement is equal to -40 m (negative because the stone is falling downwards), and the acceleration is equal to -9.8 m/s^2 (due to gravity). Rearranging the equation, we can solve for time:

-40 m = (Vertical Component of Initial Velocity * time) + (0.5 * acceleration * time^2)

Simplifying the equation:

-40 m = (15 m/s * sin(30 degrees) * time) + (0.5 * -9.8 m/s^2 * time^2)

We can solve this equation using a quadratic formula, or we can use numerical methods such as iteration, calculations, or graphing, to find the value of time.

Once we have the time, we can then calculate the magnitude of the velocity of the stone before it strikes the ground. The magnitude of the final velocity is given by:

Final Velocity = Initial Velocity + (acceleration * time)

Substituting the values:

Final Velocity = 15 m/s * cos(30 degrees) + (-9.8 m/s^2) * time

The magnitude of the velocity is the absolute value of the final velocity:

Magnitude of Velocity = |Final Velocity|

By following these steps, you can calculate the magnitude of the velocity of the stone before it strikes the ground.