A rock is thrown vertically upward from ground level at time t=0. At time t=1.3s it passes the top of the tall tower, and 1.1s later it reaches its maximum height. What is the height of the tower?

can someone please get me started....tnx in advance :)

The total time T to reach maximum height (where the velocity is zero) is 2.4 s. Use that fact to get the initial velocity Vo.

Vo = g T
Vo = 23.5 m/s

The height of the rock at any time t is
Y = Vo t - (1/2) gt^2
Knowing Vo and that Y = H (height) at t=1.3 s, you can solve for H

k tnk u so much....u r ALWAYS a big help...:)

You're welcome Mary! I appreciate your taking the time to say so.

To find the height of the tower, we need to analyze the motion of the rock and use the equations of motion. Let's break down the problem step by step.

1. First, let's define the variables:
- Initial velocity (upward): u
- Time when the rock passes the top of the tower: t1 = 1.3 s
- Time from passing the top of the tower to reaching maximum height: t2 = 1.1 s
- Maximum height of the rock: h
- Acceleration due to gravity: g (approximately 9.8 m/s^2)

2. Next, let's determine the initial velocity of the rock:
Since the rock is thrown vertically upward from the ground, its initial velocity is unknown. We only know that it passes the top of the tower at t = 1.3 s. Without the initial velocity, we can't directly calculate the height of the tower.

3. However, assuming there is no air resistance, we know that the time taken to go up and come down is the same.
Therefore, the total time it takes for the rock to reach its maximum height and then fall back down is:
t_total = t1 + t2 = 1.3 s + 1.1 s = 2.4 s

4. Now, let's find the velocity of the rock when it reaches its maximum height:
The velocity of an object at any time can be given by the equation:
v = u + at
At the maximum height, the velocity becomes zero.
Thus, when the rock reaches its maximum height, the time taken is t2 =1.1 s.
Using v = u + at and substituting the known values:
0 = u + (-g) * t2
u = g * t2

5. Now we can use the initial velocity calculated in step 4 to find the total displacement of the rock at the maximum height:
The displacement of an object can be given by the equation:
s = ut + (1/2) * a * t^2
At maximum height, the displacement becomes the height of the tower (h). So:
h = u * t2 + (1/2) * (-g) * t2^2 [Substituting values]
h = g * t2 * t2 - (1/2) * g * t2^2
h = (1/2) * g * t2^2

6. Finally, substitute the given value of t2 = 1.1 s and use the value of acceleration due to gravity (g ≈ 9.8 m/s^2) to calculate the height of the tower:
h = (1/2) * (9.8 m/s^2) * (1.1 s)^2

Calculating this will give you the height of the tower.