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a) The free body diagram is drawn in the explanation section
b) The intensity of the force applied horizontally which makes the bicycle move forward at a constant speed = 49.05 N
c) The intensity of the force applied horizontally which makes the bicycle move forward with an acceleration of 100 m/s² = 1049.05N
Explanation:The mass of the bicycle, m = 10.0 kg
Angle of inclination, θ = 30°
The free body diagram of the illustration is drawn below
The bicyce is pushed up an incline of 30°
The weight of the bicycle acts downward (because the weight of every object acts downward)
Since the bicycle is pushed up an inclined of 30°, the force has to be resolved to the vertical(mgcosθ) and horizontal(mgsinθ)
b) The net force on the bicycle is:
[tex]\sum F=mg\sin \theta+ma[/tex]If the bicycle moves at constant speed, the acceleration is 0 m/s²
a = 0m/s²
[tex]\begin{gathered} \sum F=10(9.81)\sin 30+10(0) \\ \sum F=10(9.81)(0.5) \\ \sum F=49.05N \end{gathered}[/tex]c) The intensity of the force applied horizontally which moves the bicycle forward with an acceleration of 100 m/s²
[tex]\begin{gathered} \sum F=10(9.81)\sin 30+10(100) \\ \sum F=49.05+1000 \\ \sum F=1049.05N \end{gathered}[/tex]