Kinematics and Forces Problem 1 The last time I had surgery was from a ski jumpi

Question

Kinematics and Forces

Problem 1 The last time I had surgery was from a ski jumping incident. An approximate figure of t he incident is shown below. a) Calculate the range of initial velocities leaving the jump that will result in a landing on the sloped landing? The low velocity solution will have a x displacement of 10 meters and y displacement of 0, while the high velocity solution with have a x displacement of 20 meters and a y displacement of 10 meters below the takeoff. b) For t he high velocity solution, how long is it from takeoff to landing. This is the approximate amount of time I had to think about what was going to happen. c) What is the y component of the velocity when landing at the high velocity landing (thus the knee injury)? Hints : The x displacement is given in both Cases, an expression for t can be built from this. This is also the same time for the y motion to occur. X and Y velocities are related to the velocity upon takeoff (What you are looking for). Cheek your units in the final expression, it will make you feel warm and fuzzy about your answer. There will be a small adventure in algebra to get to an expression for v^2...

Explanation / Answer

here,

let the initial velocity be u

theta = 35 degree

for low landing

let the initial velocity be u1

range , R = u1^2 * sin(2 * theta) /g

10 = u1^2 * sin(70)/9.8

u1 = 10.21 m/s

initial velocity for low v landing is 10.21 m/s

for high v landing

let the initial velocity be u2

let the time taken be t

R = u2 * cos(35) * t

24.42 = u2 * t ...(1)

h = u2*sin(theta)*t - 0.5 * g * t^2

-10 = u2 *sin(35)* t - 0.5 * 9.8 * t^2 ...(2)

from (1) and (2)

u2 = 11.05 m/s , t = 2.21 s

the initial velocity for high v landing is 11.05 m/s

(b)

the time taken for takeoff to landing is 2.21 s

(c)

y componenet of velocity is , u2 * sin(35)

the y component of the velocity in high v soluion is 6.34 m/s

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