a scientist dropped an object from a height of 200 feet. She recorded thee height of the object in 0.5 second intervals.
To analyze the height of the object dropped by the scientist, we need to know the recorded measurements at each 0.5 second interval. Please provide the recorded heights of the object at these intervals.
To analyze the data recorded by the scientist, we can use the information that the object's height was recorded in 0.5-second intervals. This means that every half-second, the scientist noted down the height of the object.
To understand the object's fall, we first need to know the position of the object at the beginning. In this case, the initial position is the height from which the object was dropped, which is given as 200 feet.
To determine the position of the object at different time intervals, we can use a simple mathematical equation that describes the motion of a falling object near the Earth's surface. This equation takes into account the initial position, time, and acceleration due to gravity.
The equation for the position of a falling object is:
h(t) = h0 - (1/2) * g * t^2
Where:
- h(t) represents the height of the object at time t.
- h0 is the initial height (200 feet in this case).
- g is the acceleration due to gravity (32.2 ft/s^2).
Let's calculate the heights of the object at different time intervals:
1) At t=0 seconds (0.5-second interval):
h(0) = 200 - (1/2) * 32.2 * (0)^2 = 200 feet
2) At t=0.5 seconds (1-second interval):
h(0.5) = 200 - (1/2) * 32.2 * (0.5)^2 = 200 - (1/2) * 32.2 * 0.25 = 200 - 4.025 = 195.975 feet
3) At t=1 second (1.5-second interval):
h(1) = 200 - (1/2) * 32.2 * (1)^2 = 200 - (1/2) * 32.2 * 1 = 200 - 16.1 = 183.9 feet
4) At t=1.5 seconds (2-second interval):
h(1.5) = 200 - (1/2) * 32.2 * (1.5)^2 = 200 - (1/2) * 32.2 * 2.25 = 200 - 36.225 = 163.775 feet
This process can be continued for any desired time interval. By using the formula h(t) = h0 - (1/2) * g * t^2, you can calculate the height at any given time.
could your question when you ask it be related to:
d = (1/2) (32) t^2
?