A skier leaves the end of a horizontal ski jump at 22.0 m/s and falls 3.20 m before landing. Neglecting friction, how far horizontally does the skier travel in the air before landing?

17.7

time to fall 3.2 m

h=1/2 g t^2

t= sqrt (2*3.2/9.8)

distance horizontal=22*timetofall

Why did the skier never land from the ski jump? Because he got cold feet! Just kidding. Let's calculate how far he traveled horizontally.

To find the horizontal distance traveled, we can use the equation:

distance = velocity × time

Since the skier is in freefall, we can use the equation for freefall time to find the time:

time = sqrt(2h/g)

where h is the vertical displacement and g is the acceleration due to gravity (approximately 9.8 m/s²).

Plugging in the given values:
h = 3.20 m
g = 9.8 m/s²

Using the equation, we can find the time:
time = sqrt(2 * 3.20 m / 9.8 m/s²) ≈ 0.64 seconds

Now, we can calculate the horizontal distance traveled using the velocity and the time:
distance = velocity × time
distance = 22.0 m/s × 0.64 s ≈ 14.08 meters

So, the skier travels approximately 14.08 meters horizontally before landing.

To find the horizontal distance traveled by the skier before landing, we can use the equations of motion for uniformly accelerated motion in two dimensions. In this case, we are neglecting friction, so only the vertical acceleration due to gravity will affect the motion vertically.

Let's break down the problem into components:

1. Vertical motion: The skier falls 3.20 m under the influence of gravity, so we can use the equation of motion:

Δy = (1/2) * g * t^2 (where Δy is the vertical displacement, g is the acceleration due to gravity, and t is the time of fall)

We know Δy = -3.20 m (negative because the skier is falling downward), and g = 9.80 m/s^2.

Plugging the numbers into the equation, we can find the time of fall:

-3.20 = (1/2) * 9.80 * t^2.

Solving for t, we find t ≈ 0.80 s.

2. Horizontal motion: Since there is no horizontal force acting on the skier in the air, its horizontal velocity remains constant.

Therefore, the horizontal distance traveled (Δx) can be found using the equation:

Δx = v_x * t (where v_x is the horizontal velocity and t is the time of fall)

We know v_x = 22.0 m/s (given in the problem) and t ≈ 0.80 s.

Plugging these numbers into the equation, we find Δx ≈ 17.6 m.

Therefore, the skier travels approximately 17.6 meters horizontally in the air before landing.

21.6

22m