in a bizzare but harmless accident, superman fell from the top of the eiffel tower. how fast was superman traveling when he hit the ground 7.80 seconds after falling
vf=g*t
g= 9.8 m/s^2
To find out the speed at which Superman was traveling when he hit the ground, we can use the equations of motion for freefall. Assuming he fell from rest at the top of the Eiffel Tower, we can use the following equation:
d = (1/2) * g * t^2
Where:
d is the distance traveled (height of the Eiffel Tower)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken (7.80 seconds)
First, we need to find the height of the Eiffel Tower. The Eiffel Tower's height is approximately 330 meters.
Now, we can plug in the values into the equation and solve for the speed:
330 = (1/2) * 9.8 * (7.80)^2
330 = 4.9 * (7.80)^2
330 = 4.9 * 60.84
330 = 298.716
To solve for the speed, we need to use one more equation:
v = g * t
v = 9.8 * 7.80
v ≈ 76.44 m/s
Therefore, Superman was traveling at approximately 76.44 m/s when he hit the ground.
To calculate Superman's speed when he hit the ground, we need to use the laws of motion and apply the equation for free-fall motion.
The equation for free-fall motion is: d = (1/2) * g * t^2, where d is the distance fallen, g is the acceleration due to gravity (about 9.8 m/s^2 on Earth), and t is the time of fall.
Given that Superman fell for 7.80 seconds, we can rearrange the equation to solve for d: d = (1/2) * g * t^2.
Now, we need to know the height of the Eiffel Tower to determine the distance Superman fell. The Eiffel Tower has an overall height of 330 meters.
Using the equation d = (1/2) * g * t^2, and plugging in the values, we have: 330 = (1/2) * 9.8 * (7.80^2).
Simplifying the equation, we have: 330 = 0.5 * 9.8 * 60.84.
Now, divide both sides of the equation by 0.5 * 9.8 to find the value of t^2: t^2 = 330 / (0.5 * 9.8 * 60.84).
Taking the square root of both sides will give us the value of t: t = √(330 / (0.5 * 9.8 * 60.84)).
Calculating this value, t ≈ 4.3 seconds.
Now that we know the time it took for Superman to fall from the top of the Eiffel Tower is approximately 4.3 seconds, we can calculate his speed at impact.
The equation for speed is: v = g * t.
Substituting the values, v = 9.8 * 4.3.
Therefore, Superman was traveling at approximately 42.14 m/s when he hit the ground 7.8 seconds after falling from the top of the Eiffel Tower.