a rock is thrown vertically upward from ground level at t=0. At t= 1.5s, it passes the top of a tall tower and 1.0 s later, it reached its maximum height. what is the height of the tower?

Tr = 1.5 + 1 = 2.5 s. = Rise time or time to reach max ht.

V = Vo + g*Tr = 0
Vo -9.8*2.5 = 0
Vo = 24.5 m/s. = Initial velocity.

h max = Vo*t + 0.5g*t^2 =
Vo*2.5 - 4.9*2.5^2 = 2.5Vo -

Tr = 1.5 + 1 = 2.5 s. = Rise time or time to reach max ht.

V = Vo + g*Tr = 0
Vo -9.8*2.5 = 0
Vo = 24.5 m/s. = Initial velocity.

h = Vo*t + 0.5g*t^2 =
24.5*1.5 - 4.9*1.5^2 = 25.7 m. = Ht. of
the tower.

Please disregard my 5:24 PM post.

To determine the height of the tower, we'll need to analyze the rock's motion. Let's break down the information provided:

1. The rock is thrown vertically upward from ground level at t=0.
2. At t=1.5s, it passes the top of the tall tower.
3. 1.0 second later, it reaches its maximum height.

Let's calculate the height step by step:

Step 1: Find the time to reach maximum height.
Since the rock takes 1.0 second to reach its maximum height after passing the top of the tower (t=1.5s), we can assume that it took 2.5 seconds (1.5s + 1.0s) to reach its maximum height.

Step 2: Calculate the maximum height.
To find the maximum height, we need to use the equation for vertical motion:
h(t) = h0 + v0t - 0.5gt^2,

where:
h(t) = height at time t,
h0 = initial height (ground level),
v0 = initial velocity,
t = time, and
g = acceleration due to gravity.

In this case, the rock is thrown vertically upward, so the initial velocity is positive (upward). At maximum height, the velocity becomes zero.

Therefore, the equation becomes:
0 = h0 + v0(2.5s) - 0.5g(2.5s)^2.

Since we know that the velocity at maximum height is zero, we can simplify the equation to:
0 = h0 - 0.5g(2.5s)^2.

Solving for h0 (initial height), we can rewrite the equation as:
h0 = 0.5g(2.5s)^2.

Step 3: Calculate the height of the tower.
Now, we need to consider the time it took for the rock to pass the top of the tower, which is 1.5 seconds.

Using the same equation, but substituting t with 1.5s, we have:
h(1.5s) = h0 + v0(1.5s) - 0.5g(1.5s)^2.

Since the rock initially starts from the ground, h0 is equal to zero.

0 = 0 + v0(1.5s) - 0.5g(1.5s)^2.

Simplifying further, we get:
v0 = 0.5g(1.5s)^2 / (1.5s).

Step 4: Substitute v0 into the equation for h0.
By substituting the value of v0 into the equation we derived for h0, we can find the height of the tower:
h0 = 0.5g(2.5s)^2.

Note that we already have the equation for v0 from step 3.

By substituting the value for g (acceleration due to gravity) and solving these equations, we can find the height of the tower.