Final answer:
To find the height of the tower, we use the kinematic equation for uniformly accelerated motion. The initial velocity is determined using the time to reach the maximum height, and this velocity is then used to calculate the height of the tower, which is approximately 40.131 m. None of the provided answer choices match this result.
Step-by-step explanation:
To determine the height of the tower that the rock passes after 1.3 seconds, we need to use the kinematic equation for uniformly accelerated motion, which is appropriate for objects moving under the influence of gravity:
S = ut + ½ at²
where:
- S is the displacement (height of the tower in this case)
- u is the initial velocity (which we don't know yet)
- t is the time (1.3 s until it passes the tower)
- a is the acceleration due to gravity (9.8 m/s², but negative because it's directed downwards)
We also know the total time to reach the maximum height is 1.3 s + 2.5 s = 3.8 s. At maximum height, the velocity of the rock is 0 m/s. Using this information, we can calculate the initial velocity u:
0 = u + at
0 = u - 9.8m/s² × 3.8s
u = 9.8m/s² × 3.8s
u = 37.24 m/s
Now we can calculate the height of the tower using the initial velocity and the time it takes to pass the tower:
S = ut + ½ at²
S = 37.24 m/s × 1.3 s + ½ (− 9.8 m/s²) × (1.3 s)²
S = 48.412 m - ½ × 9.8 m/s² × 1.69 s²
S = 48.412 m - 8.281 m
S = 40.131 m
The height of the tower is approximately 40.131 m; therefore, the correct answer is not listed among the options. Either there is an error in the question or the answer choices.