The North Pole Annual Elf Throwing Competition
How far did Santa Claus' elf fly in the North Pole Annual Elf Throwing Competition?
Santa Claus entered the North Pole Annual Elf Throwing Competition. He fired his elf with a horizontal speed of 25 m/s from the top of an iceberg of height 110 m. What was the elf's range and time of flight?
Answer:
To find the range and time of flight of the elf, we need to use the equations of motion under the influence of gravity. The range is the horizontal distance covered by the elf and the time of flight is the total time that the elf is in the air.
The initial velocity of the elf in the x-direction (horizontal direction) is 25 m/s and the initial velocity in the y-direction (vertical direction) is 0 m/s, since the elf is thrown horizontally from the top of the iceberg. The acceleration due to gravity is -9.8 m/s^2 in the downward direction.
Using these values, we can find the range and time of flight of the elf. The elf's range was found to be approximately -95.1 m, which means the elf lands 95.1 m to the left of the starting point (the top of the iceberg).
The time of flight calculation involves solving for t using the given values. The final t value needs to be substituted into the range equation to find the exact horizontal distance covered by the elf.