A 51-kg vampire and 139-kg werewolf clash during the Feat of Strength part of the annual celebration of Festivus. The werewolf velocity just before the clash is 6 m/s and is directed upwards, while the vampire velocity at the moment of the collision is 10m/s and is directed down. They clash in mid-air exactly 11 meters above the ground. Vampire will starts feeding on werewolf at the moment of collision, and will not stop until they hit the ground. Find how long (in s) will the vampire feast on the werwolf? Calculate the answer to two decimal places
To find how long the vampire will feast on the werewolf, we need to calculate the time it takes for them to hit the ground. We can use the equations of motion to solve this problem.
The initial velocity of the werewolf, v1 = 6 m/s. The initial velocity of the vampire, v2 = -10 m/s (negative sign indicates downward direction).
The height of the collision, h = 11 meters.
We know that the acceleration due to gravity, g = 9.8 m/s^2, acts downward.
Let's use the equation of motion for vertical displacement to find the time it takes for both the vampire and werewolf to hit the ground:
h = (v1 + v2) * t / 2
Simplifying the equation, we get:
2h = (v1 + v2) * t
Plugging in the values:
2 * 11 = (6 - 10) * t
22 = -4t
Dividing by -4, we get:
t = -22 / -4
t = 5.5 seconds
Therefore, the vampire will feast on the werewolf for approximately 5.5 seconds.