A stone thrown upward at the top of the tower reaches the ground after 5 sec. A second stone is thrown down with the same speed and reaches ground in 3 sec. What is the height of the tower

it takes the 1st stone 2 s to reach its peak and return to the top of the tower, now going downward with the same velocity as the 2nd stone

that velocity is 9.8 m/s

when it reaches the ground, its velocity is 39.2 m/s...4 s * 9.8 m/s

its average velocity is 24.5 m/s
... (9.8 + 39.2) / 2

the distance (height) is 73.5 m
... 3 s * 24.5 m/s

To find the height of the tower, we need to calculate the time it takes for the stone to reach the highest point (when thrown upward) and then use that time to calculate the height of the tower.

Let's first calculate the time it takes for the stone to reach the highest point when thrown upward. We know that the total time of flight is 5 seconds. Since the stone is in the air for the same amount of time while going up and coming down, the time to reach the highest point would be half of the total time of flight, which is 5/2 = 2.5 seconds.

Now that we have the time it takes for the stone to reach the highest point, we can find the initial velocity (or speed) with which the stone was thrown upward. We use the equation of motion:

v = u + at

where:
- v is the final velocity (which is 0 at the highest point)
- u is the initial velocity
- a is the acceleration due to gravity (which is approximately 9.8 m/s^2)
- t is the time taken (which is 2.5 seconds)

Since the final velocity is 0 m/s, we can rearrange the equation to solve for the initial velocity:

0 = u + (9.8 × 2.5)

Rearranging again:

u = -9.8 × 2.5

u = -24.5 m/s (negative sign indicates the direction is opposite to the positive upward direction)

Now we can use the equation of motion to find the height of the tower, assuming the stone was thrown from the top of the tower:

s = ut + (1/2)at^2

where:
- s is the height of the tower
- u is the initial velocity
- t is the time taken (which is 5 seconds, as the stone reaches the ground after 5 seconds)
- a is the acceleration due to gravity (which is -9.8 m/s^2, since the stone is moving downward)

Substituting the values:

s = -24.5 × 5 + (1/2)(-9.8)(5^2)

Simplifying:

s = -122.5 + (-122.5)

s = -245 meters

The height of the tower is 245 meters.