While exploring the canopy of the rainforest in equatorial South America, Anastasia falls from a branch 40.0 meters high. Exactly 1.1 seconds later Joe falls from the same branch. How high above the ground is Joe when Anastasia splats into the mud below?
15.12
To find out how high Joe is when Anastasia splats into the mud below, we can use the equations of motion. The equation we will use is:
h = vi*t + (1/2)*g*t^2
Where:
h is the height above the ground
vi is the initial velocity (0 m/s for both Anastasia and Joe)
t is the time in seconds
g is the acceleration due to gravity (approximately 9.8 m/s^2)
For Anastasia, we can substitute the values:
h_Anastasia = vi*t + (1/2)*g*t^2
h_Anastasia = 0*1.1 + 0.5*9.8*(1.1)^2
h_Anastasia = 0 + 0.5*9.8*1.21
h_Anastasia = 5.735 m
So, Anastasia is 5.735 meters above the ground when she splats into the mud below.
To find the height of Joe, we can subtract the height at which Anastasia splats from the branch height:
h_Joe = 40.0 - 5.735
h_Joe = 34.265 m
Therefore, Joe is approximately 34.265 meters above the ground when Anastasia splats into the mud below.
To determine the height above the ground at which Joe is when Anastasia hits the ground, we can use the equations of motion in physics.
Let's assume the initial velocity of each person is zero, and the acceleration due to gravity is approximately 9.8 m/s^2. We will also consider upward direction as positive.
Using the equation of motion:
h = ut + (1/2)gt^2
where:
- h is the height (to be determined)
- u is the initial velocity (which is zero)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time (1.1 seconds)
For Anastasia:
hA = 0 + (1/2) * 9.8 * (1.1)^2
hA = 0 + 0.5 * 9.8 * 1.21
hA = 5.69 meters
So, Anastasia falls to a height of 5.69 meters.
Now, let's calculate Joe's height:
hJ = 40 - hA
hJ = 40 - 5.69
hJ ≈ 34.31 meters
Therefore, when Anastasia hits the ground, Joe is approximately 34.31 meters above the ground.
40=1/2 g t^2
solve for t
h=1/2 g (t-1.1)^2