Answer:
Vertical height = 5 m
Explanation:
Given:
There is no frictional losses. So, energy is conserved.
Acceleration due to gravity (g) = 10 m/s²
Initial velocity at the bottom of hill (u) = 10 m/s
Final velocity at the moment it stops on the hill (v) = 0 m/s
Initial height at the bottom (h₁) = 0 m
Final height (h₂) = ?
As there are no frictional losses, the total energy remains conserved.
So, increase in potential energy is equal to decrease in kinetic energy.
Increase in potential energy is given as:
[tex]\Delta U=mg(h_2-h_1)=10mh_2[/tex]
Decrease in kinetic energy is given as:
[tex]\Delta KE=\frac{1}{2}m(u^2-v^2)=\frac{1}{2}m(10^2)=50m[/tex]
Now, [tex]\Delta U =\Delta KE[/tex]
⇒ [tex]10mh_2=50m[/tex]
⇒ [tex]h_2=\frac{50}{10}=5\ m[/tex]
Therefore, the vertical height of the bicycle when it stops coasting is 5 m.
