1EXS 387 - BiomechanicsDr. MoranTuesday February 6, 2007Spring 2007Linear KinematicsPart IIEXS 387 2Lecture Objectives• Human Gait Kinematics• Stride Rate• Stride Length• Projectile Motion• Horizontal/Vertical Components• Factors Influencing– Gravity– Air Resistance– Trajectory– Projection Angle– Laws of Constant Acceleration2EXS 387 3What do we remember?• A sprinter is running a 100m race. He pushes off the blocks andspeeds up maximum speed of 11 m/s at 5 seconds, holds for 3 seconds before slowing until he crosses the finish line at 10.7 seconds.a.) What was average acceleration from the start to maximum speed?b.) What was acceleration from 5 to 8 seconds of race?c.) In which direction was the sprinter’s acceleration during the last 2.7 seconds?EXS 387 4Solutiona.) b.) c.)3EXS 387 5Human Gait• Def: The manner or style of walking• Speed of Gait = Stride Length (SL) x Stride Rate (SR)• Stride Length: • Stride Rate: # of strides per given unit of time• Typically the following holds:• Adults in a rush will • Why wouldn’t toddlers or elderly want to increase SL?BALANCE ISSUES…EXS 387 6Running Kinematics• SL is a function of many variables» Body height» Footwear» Level of Fatigue» Injury history» Stiffness of running surface• At a slow pace recreational runners typically increase first • For more serious runners a preferred SR is used for slow to moderate paces.4EXS 387 7Running Kinematics(con’t)EXS 387 8Sport-Specific Kinematics• Dillman (1985)• The best sprinters have extremely high SR and average SL• A high SR decreases the amount of contact time between the foot and ground decreasing the amount of time to push off the ground• McCaw et al. (1987)5EXS 387 9Projectile Motion• Any body projected into the air is a projectile• It is easier to analyze a projectile’s horizontal and vertical components separately• The vertical component is affected by gravityEXS 387 10Gravity• Accelerates bodies in a vertical direction towards the surface of earth• Constant acceleration –• Consider you threw a ball straight up in the air. Draw three graphs of:• Vertical Displacement vs Time• Vertical Velocity vs Time• Vertical Acceleration vs Time6EXS 387 11Factors Influencing Projectile Trajectory• Angle of Projection•• Projection AngleEXS 387 12Angle of Projection• Def: the direction at which a body is projected with respect to the horizontal7EXS 387 13Projection Speed• Determines the of a projectile’s trajectoryEXS 387 14Analyzing Projectile Motion• Assume that the horizontal component of velocity is throughout flight•• Laws of Constant Acceleration• v2= v1+ at• d = v1t + ½ at2•advv 22122+=v = veloctiya = acceleration due to gravityt = timed = distance8EXS 387 15Sample Problem #1Horizontal Component• A placekicker is attempting to kick a 29m field goal. If the ball was kicked with a horizontal component of initial velocity of 18 m/s and had a flight time of 2 s was the kick long enough clear the goalposts?EXS 387 16Sample Problem #2Vertical Component• A volleyball is deflected vertically by a player in a game housed in a gym with a 10m ceiling. If the initial velocity of the ball is 15m/s, will the ball hit the ceiling?a = -9.81 m/s29EXS 387 17Sample Problem #3Putting it All Together• A ball is kicked at an angle of 35 with an initial velocity of 12 m/s. How high and how far does the ball go?Step #1: Draw PictureStep #2: Decompose velocity into componentsStep #3: Write out knowns and consider three laws of constant accelerationEXS 387 18Problems on Own• Page 351 #7 -