A hoodlum throws a stone verticlly downwarsd with an inital speed of 12m/s from the roof of a building,30m above the ground

a)How long does it take the stone to reach the ground?

b)What is the speed of the stone at impact?

What would be the 2 equations for this problem?

a) Solve
Y = 30 - 12 t - (1/2) g t^2 = 0 for the elapsed time, t.
g = 9.8 m/s^2.
Take the positive root of the quadratic equation you get.
b) V (at impact) = Vinitial + g t
= -12 - 9.8 t
It will be a negative number (downwards)

1.54 seconds

27.092 m/s

To solve this problem, we can use two equations of motion that relate the position, velocity, time, and acceleration of the stone.

1) The equation for the stone's vertical position (Y) as a function of time (t) is:

Y = initial height + initial velocity * t - (1/2) * acceleration * t^2

In this case, the initial height is 30m, the initial velocity is -12m/s (since it is thrown downward), and the acceleration is -9.8m/s^2 (due to gravity acting in the downward direction). This equation represents a quadratic equation, and by setting Y to zero, we can solve for the time it takes for the stone to reach the ground.

2) The equation for the stone's velocity (V) as a function of time (t) is:

V = initial velocity + acceleration * t

In this case, the initial velocity is -12m/s (again, negative because the stone is thrown downward) and the acceleration is -9.8m/s^2. This equation will give us the speed of the stone at impact.

a) To find the time it takes for the stone to reach the ground, we set Y to zero in the first equation and solve for t:

0 = 30 - 12t - (1/2) * 9.8 * t^2

Simplifying and rearranging the equation, we get a quadratic equation:

(1/2) * 9.8 * t^2 + 12t - 30 = 0

To solve this equation, we can use the quadratic formula or factoring. By taking the positive root of the equation, we will get the time it takes for the stone to reach the ground.

b) To find the speed of the stone at impact, we can use the second equation:

V = -12 - 9.8t

At impact, the stone will be at the ground, so t will be the time obtained from part a) which represents the time it takes for the stone to reach the ground. Here, the negative sign indicates that the stone is moving downward, which makes sense since it is thrown downward.

By substituting the value of t into the equation, we can find the speed of the stone at impact.