While swinging on the wrecking ball, a student notices that, at first, the wrecking
ball is in line with her birdbath when it is at a peak in its trajectory, and in line with her front door at the lowest point in the trajectory. However, since drag is acting against the wrecking ball’s motion, 3.00 minutes later the peak of the wrecking ball’s trajectory is in line with her garden gnome, the halfway point between her birdbath and front door. How much longer will it take for the peak of the ball’s trajectory to be halfway between her garden gnome and her front door? From the time she begins to watch the wrecking ball, how long will it take for the trajectory peak to be in line with the edge of her welcome mat, which is one tenth of the distance from her front door to the bird bath?
mass of ball = to 720kg and velocity of ball and her is 1.90m/s
To answer the first question, we need to understand the motion of the wrecking ball and analyze it based on the given information.
Let's break down the problem into different parts:
1. Finding the time it takes for the peak of the trajectory to be halfway between the garden gnome and the front door:
Given that at first, the wrecking ball is in line with the birdbath at the peak of its trajectory, and later, after 3.00 minutes, it is in line with the garden gnome at the same point in the trajectory.
To find how much longer it will take for the peak to be halfway between the garden gnome and the front door, we need to calculate the difference in time between when it was in line with the birdbath and when it was in line with the garden gnome.
Let's assume the time it takes for the peak to be in line with the birdbath as t1 and the time it takes for the peak to be in line with the garden gnome as t2.
So, the time it took for the peak to be halfway between the garden gnome and the front door is:
t2 - t1 = 3.00 minutes
2. Finding the total time from the start to the peak of the trajectory aligning with the edge of the welcome mat:
To find this time, we need to determine the distance between the front door and the birdbath, and then calculate one-tenth of this distance, which will be the distance from the front door to the edge of the welcome mat.
From the given information, we know that the peak of the trajectory aligning with the front door is at the lowest point, and the distance from the front door to the birdbath is involved.
So, let's assume the time it takes for the peak of the trajectory to be in line with the edge of the welcome mat as t3.
The distance from the front door to the birdbath can be represented as d1, and the distance from the birdbath to the garden gnome as d2.
Therefore, the distance from the front door to the edge of the welcome mat will be d1/10.
To determine the total time from the start to the peak aligning with the edge of the welcome mat, we need to add t1, t2, and t3.
Essentially, we need more specific information or additional equations to find the exact values of t1, t2, and t3.
If you provide the equations or additional details related to the motion of the wrecking ball, we can help you solve the problem with more accuracy.