You are enjoying a day at the amusement park, riding a roller coaster, when suddenly a section of track up ahead crashes to the ground. You estimate that the cart is travelling at 5 m/s horizontally on the track before you begin to fall through the air. If the coaster leaves the track at a point 90 meters off the ground, how far from the base of the coaster will you (and the rest of the car) land?

To find the horizontal distance from the base of the coaster where you will land, we can use the horizontal velocity and the time of flight. First, let's calculate the time it takes for you to fall to the ground.

The initial velocity in the vertical direction (when you leave the track) is zero, and we can assume that the only force acting on you is gravity, which accelerates objects downward at 9.8 m/s².

We can use the equation of motion for free fall:
h = (1/2)gt²

Where:
- h is the height (90 meters)
- g is the acceleration due to gravity (9.8 m/s²)
- t is the time

Rearranging the equation and solving for t:
t = √((2h)/g)

Substituting the values:
t = √((2 * 90) / 9.8)
t ≈ √(180 / 9.8)
t ≈ √18.37
t ≈ 4.29 seconds

Now that we have the time of flight, we can find the horizontal distance traveled by multiplying the horizontal velocity by the time:
Distance = Velocity * Time
Distance = 5 m/s * 4.29 s
Distance ≈ 21.45 meters

Therefore, you will land approximately 21.45 meters horizontally away from the base of the coaster.