A small rock is thrown vertically upward with a speed of 13.0 m/s from the edge of the roof of a 20.0 m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected.

A.) What is the speed of the rock just before it hits the street?

B.) How much time elapses from when the rock is thrown until it hits the street?

a) consider energy

Intial KE+ initailPE= finalKE
1/2 m 13^3+ mg*20=1/2 m vf^2 solve for Vf.

b) time?
avg veloctity= (-13+vf )/2

time= distance/avg velocity= 2*20/(Vf-13)

A stone was thrown upward from the cornice of a tall building 50 m in height with an initial speed. It misses the cornice on its way down and strikes the ground 10 seconds after it was thrown. Find the initial speed.

A.) To find the speed of the rock just before it hits the street, we can use the equation of motion for vertical motion. The equation is given by:

v² = u² + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement

In this case, the rock is thrown vertically upward, so the initial velocity (u) is 13.0 m/s and the displacement (s) is equal to the height of the building, which is 20.0 m. Also, the acceleration (a) is equal to the acceleration due to gravity, which is approximately 9.8 m/s².

Substituting these values into the equation, we have:

v² = 13.0² + 2(-9.8)(20.0)

v² = 169.0 + 2(-9.8)(20.0)

v² = 169.0 - 392.0

v² = -223.0

Taking the square root of both sides, we get:

v ≈ √(-223.0)

However, the square root of a negative number is not defined in real numbers. Therefore, the equation does not yield a real solution. This means that the rock does not hit the street.

B.) Since the rock does not hit the street, the time elapsed from when the rock is thrown until it hits the street is infinity.

To find the answer to these questions, we can use the equations of motion for objects in free fall. Here's how we can approach these:

A.) What is the speed of the rock just before it hits the street?

To find the speed of the rock just before it hits the street, we need to determine its final velocity. We know the initial velocity when the rock was thrown vertically upward, but we need to find its final velocity at the point of impact.

First, let's find the time it takes for the rock to reach its highest point. We can use the equation:

v = u + at

where:
v = final velocity = 0 m/s (at the highest point, the velocity is momentarily zero)
u = initial velocity = 13.0 m/s (upward)
a = acceleration due to gravity = -9.8 m/s^2 (negative since it acts in the opposite direction of the initial velocity)
t = time

Rearranging the equation, we have:

t = (v - u) / a

t = (0 - 13.0) / -9.8
t ≈ 1.33 seconds

Now, let's find the time it takes for the rock to fall back down from its highest point to the ground. This is the same time it took to go up, so t = 1.33 seconds.

Using this time, we can find the final velocity (v) at the point of impact using the equation:

v = u + at

where:
v = final velocity
u = initial velocity (which is zero when the rock starts falling down)
a = acceleration due to gravity

v = 0 + (-9.8) * 1.33
v ≈ -13.0 m/s

Since the velocity is negative, we can take the magnitude to find the speed:

Speed = |v| = |-13.0| = 13.0 m/s

Therefore, the speed of the rock just before it hits the street is 13.0 m/s.

B.) How much time elapses from when the rock is thrown until it hits the street?

To find the time it takes for the rock to hit the street, we need to consider the entire duration of its journey.

The total time can be found by adding together the time it takes for the rock to reach its highest point (which we already calculated to be 1.33 seconds) and the time it takes to fall back down to the street level.

Since the total journey is symmetrical, the time taken to reach its highest point is the same as the time taken to return to the ground. Therefore, the total time is:

Total time = 1.33 seconds + 1.33 seconds = 2.66 seconds

Hence, the time elapsed from when the rock is thrown until it hits the street is approximately 2.66 seconds.