Eddie the Eagle, British Olympic ski jumper, is attempting his most mediocre jump yet. After leaving the end of the ski ramp, he lands downhill at a point that is displaced 62.2 m horizontally from the edge of the ramp. His velocity just before landing is 29.0 m/s and points in a direction 39.0 below the horizontal. Neglect any effects due to air resistance or lift.
What was the magnitude of Eddie's initial velocity as he left the ramp? (in m/s)
Determine Eddie's initial direction of motion as he left the ramp, measured relative to the horizontal. (in deg)
Calculate the height of the ramp's edge relative to where Eddie landed. (in m)
See Related Questions: Fri, 1-31-14,
10:23 PM.
To solve these physics problems, we can use the principles of projectile motion. Let's break it down step by step.
1. Finding the magnitude of Eddie's initial velocity:
We know that the horizontal displacement is 62.2 m, and the velocity just before landing is 29.0 m/s. Considering the horizontal motion, we can use the formula for horizontal displacement:
Δx = v₀x * t,
where:
Δx = horizontal displacement = 62.2 m,
v₀x = initial horizontal velocity,
t = time of flight.
Since there is no horizontal acceleration, the horizontal velocity remains constant throughout the motion. Therefore, v₀x = v₁x, where v₁x is the horizontal velocity just before landing.
From the given information, we know that v₁x = 29.0 m/s.
2. Finding the initial direction of motion:
The angle below the horizontal, given as 39.0°, represents the angle of the velocity vector just before landing. To find the initial direction of motion, we need to consider the angle of the initial velocity vector.
Using trigonometry, we can find the angle as follows:
tan(θ) = v₀y / v₀x,
where:
θ = angle of the initial velocity vector,
v₀y = initial vertical velocity,
v₀x = initial horizontal velocity.
We can rearrange the equation and substitute the given values:
θ = arctan(v₀y / v₀x).
As we know the inclination angle below the horizontal, we can determine the angle above the horizontal by subtracting it from 90°:
θ = 90° - 39.0°.
3. Calculating the height of the ramp's edge:
To find the height of the ramp's edge relative to where Eddie landed, we need to consider the vertical motion. Since there is no vertical acceleration when neglecting air resistance, we can use the equation:
Δy = v₀y * t + (1/2) * g * t^2,
where:
Δy = vertical displacement = height,
v₀y = initial vertical velocity,
t = time of flight,
g = acceleration due to gravity = 9.8 m/s^2.
Since Eddie lands at the same height as he starts, Δy = 0. In addition, we know that the time of flight is the same for vertical and horizontal motion, so we can use the time of flight obtained from the horizontal motion calculations.
0 = v₀y * t + (1/2) * g * t^2.
Solving this equation will give us the height of the ramp's edge relative to where Eddie landed.
Now, using the information provided, you can substitute the values into the relevant equations to find the answers.