A drowsy cat spots a flowerpot that sails first up and then down past an open window. The pot was in view for a total of 0.37 s, and the top-to-bottom height of the window is 2.20 m. How high above the window top did the flowerpot go?
S= ut +(1/2)at^2
S= (0)(0.215) + (0.5)(9.8)(0.215)^2
S= 0.2265025m
That's what I did and the site tells me I'm wrong. Please help.
The pot spends T = 0.185s going up and 0.185s going down past the window.
The average speed passing by the window is 2.20 m/0.185s = 11.89 m/s.
During passage, the pot increases speed by T*g = 0.185*9.81 = 1.815 m/s
The speed is therefore 12.80 m/s at the bottom of the window and 10.98 m/s at the top of the window.
The 10.98 m/s speed at the top of the window allows it to rise another 10.98^2/(2g)= 6.15 m past the top of the window
To solve this problem, we need to determine the height above the window top that the flowerpot reached during its trajectory. Let's break down the problem step by step:
1. First, we need to identify the relevant quantities given in the problem:
- Total time the pot was in view: t = 0.37 s
- Top-to-bottom height of the window: h = 2.20 m
2. Since the pot moves both upwards and downwards, we need to consider the time taken to go up and then come back down. The time spent going up is the same as the time spent coming down when neglecting air resistance.
3. Therefore, the time spent going up is given by t/2, as it represents half of the total time. In this case, t/2 = 0.37 s / 2 = 0.185 s.
4. Now, we can calculate the height reached during the upward journey using the formula:
S = ut + (1/2)at^2
In this case, the initial velocity (u) is 0 since the pot starts from rest. The acceleration (a) is the acceleration due to gravity, approximately 9.8 m/s^2.
Plugging in the values, we get:
S = (0)(0.185) + (1/2)(9.8)(0.185)^2
S = 0 + 0.5(9.8)(0.034225)
S ≈ 0.1677215 m
5. Finally, we need to find the height above the top of the window, so we subtract the height reached during the upward journey from the total height of the window:
Height above window top = h - S
Height above window top = 2.20 m - 0.1677215 m
Height above window top ≈ 2.0322785 m
Therefore, the flowerpot went approximately 2.032 m above the top of the window.