A ball is thrown vertically upward from a window with an initial velocity of 10m/s. if it hits the ground below the window 5.0s later, what is the height of the window...can you tell me the steps on how to do this please...

To find the height of the window, we can use the following steps:

Step 1: Identify the known values:
- Initial velocity (u) = 10 m/s (upward)
- Time taken to reach the ground (t) = 5.0 s
- Acceleration due to gravity (g) = -9.8 m/s² (considered negative as it acts downward)

Step 2: Calculate the final velocity (v) when the ball hits the ground.
Using the kinematic equation: v = u + gt
Substitute the known values:
v = 10 m/s + (-9.8 m/s²) * 5.0 s
v = 10 m/s - 49 m/s
v = -39 m/s

Step 3: Calculate the maximum height (h) reached by the ball.
Using the kinematic equation: v² = u² + 2gh
Substitute the known values:
(-39 m/s)² = (10 m/s)² + 2 * (-9.8 m/s²) * h
1521 m²/s² = 100 m²/s² - 19.6 m/s² * h
1521 m²/s² - 100 m²/s² = -19.6 m/s² * h
1421 m²/s² = -19.6 m/s² * h
Divide both sides by -19.6 m/s²:
-1421 m²/s² / -19.6 m/s² = h
h ≈ 72.4 meters

Step 4: Determine the height of the window.
The height of the window would be equal to the maximum height reached by the ball, which is approximately 72.4 meters.

To find the height of the window, we need to understand the motion of the ball. We can use the equations of motion to solve this problem step by step.

Step 1: Understand the initial conditions and variables
- Initial velocity (u) = 10 m/s (upward)
- Time taken to hit the ground (t) = 5.0 s
- Acceleration due to gravity (g) = 9.8 m/s^2 (downward)

Step 2: Find the final velocity of the ball when it hits the ground
- The final velocity (v) of the ball when it hits the ground is 0 m/s (since it comes to a stop).
- Use the equation v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

v = u + gt
0 = 10 + (-9.8)(5)
0 = 10 - 49
-49 = -10
-49 + 10 = 0
-39 = 0

Therefore, the final velocity is 0 m/s.

Step 3: Calculate the maximum height reached by the ball
- At the maximum height, the ball will have zero vertical velocity.
- Using the equation v = u + gt, we can find the time it takes to reach the maximum height.

v = u + gt
0 = 10 + (-9.8)t
0 = 10 - 9.8t
-10 = -9.8t
10 = 9.8t
t = 10 / 9.8
t ≈ 1.02 s

The ball takes around 1.02 seconds to reach its maximum height.

Step 4: Calculate the maximum height using the time calculated in step 3
- At the maximum height, the vertical displacement (s) is what we need to find.
- Again, using the equations of motion, we can find the displacement using the equation v^2 = u^2 + 2as, where s is the displacement.

u = 10 m/s
v = 0 m/s
t = 1.02 s (time calculated in step 3)
a = -9.8 m/s^2 (acceleration due to gravity)

0 = 10^2 + 2(-9.8)s
0 = 100 - 19.6s
19.6s = 100
s = 100 / 19.6
s ≈ 5.1 m

Therefore, the maximum height reached by the ball is approximately 5.1 meters.

Step 5: Calculate the height of the window
- The height of the window is the same as the maximum height reached by the ball.
- So, the height of the window is approximately 5.1 meters.

In conclusion, the height of the window from which the ball is thrown vertically upward is approximately 5.1 meters.

assume all heights are from the middle of the window.

hf=hi+vi*t-1/2 g t^2
hf=unknown
hi=zero
vi=10
t=5
g =-9.8m/s^2
calculate