3. A hurdler with a mass of 85kg jumps into the air at an angle of 60 degrees to

Question

3. A hurdler with a mass of 85kg jumps into the air at an angle of 60 degrees to the horizontal with a 10 m/s2 initial acceleration. We are curious about the ground reaction forces causing this motion. (Hint: GRFx = max; GRFy + W = may)

3.1. Calculate the vertical acceleration.

3.2. Calculate the horizontal acceleration.

3.3. Calculate the vertical ground reaction force that caused this motion.

3.4. Calculate the horizontal ground reaction force that caused this motion.

3.5. Calculate the resultant ground reaction force that caused this motion.

3.6. What is the angle of the resultant ground reaction force?

Explanation / Answer

hurdler mass m=85 kg

initial acceleration a=10 m/sec^2

angle, theta=60 degrees ( w r to horizontal)

3.1)

vertical acceleration, ay=a*sin(theta)

ay=10*sin(60)

ay=8.66 m/sec^2

3.2)

horizontal acceleration, ax=a*cos(theta)

ax=10*cos(60)

ax=5 m/sec^2

3.3)

vertical ground reaction force,

m*ay=Fy-W

Fy=m*ay-W

Fy=85*8.66-(85*9.8)

Fy=-96.9 N

3.4)

horizontal reaction force,

Fx=m*ax

Fx=85*5

Fx=425 N

3.5)

net ground reaction force,

Fnet=sqrt(Fx^2+Fy^2)

=sqrt((-96.9)^2+425^2)

=435.9 N

3.6)

angle=arctan(Fy/Fx)

=arctan(-96.9/425)

=-12.8 degrees

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