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 using the following equations:
Range:
x = x0 + v0x*t
Where x is the range, x0 is the initial position (in this case, x0 is 0 since the elf is thrown from the top of the iceberg), v0x is the initial velocity in the x-direction (25 m/s), and t is the time of flight.
Time of flight:
y = y0 + v0y*t + (1/2)at^2
Where y is the vertical position of the elf, y0 is the initial position (in this case, y0 is 110 m since the elf is thrown from the top of the iceberg), v0y is the initial velocity in the y-direction (0 m/s), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight.
We can solve for t in the second equation and then substitute it into the first equation to find the range.
Solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Where y is the vertical position of the elf (0 m since the elf lands on the ground), y0 is the initial position (110 m), v0y is the initial velocity in the y-direction (0 m/s), and a is the acceleration due to gravity (-9.8 m/s^2).
Substituting this expression for t into the first equation:
x = x0 + v0x*((-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a))
Plugging in the values:
x = 0 + 25*((-0 + sqrt(0^2 - 4*(-9.8)(110))) / (2(-9.8)))
Simplifying:
x = 25*(sqrt(5832) / -19.6)
x = 25*(sqrt(5832) / -19.6)
x = (25*74.6) / -19.6
x = 1865.4 / -19.6
x = -95.1 m
So, the range of the elf is approximately -95.1 m. This means that the elf lands 95.1 m to the left of the starting point (the top of the iceberg).
The time of flight can be found by solving for t in the second equation:
t = (-v0y +/- sqrt(v0y^2 - 4a(y0 - y))) / (2*a)
Plugging in the values:
t =
Step-by-step explanation: