Question

A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and the rider is 85 kg. Find the kinetic energy of the bike and the rider. If the rider coasts up the hill calculate the height at which the bike will come to a stop. (h=PE/mgh)
Please help me!! this is due in like 20 minutes!!

Answer 1

KE=3070.625 J

Height = 3.686 m

Further explanation

mass of bike+rider=85 kg

velocity = 8.5 m/s

$\tt KE=\dfrac{1}{2}mv^2\\\\KE=\dfrac{1}{2}\times 85\times 8.5^2\\\\KE=3070.625~J$

Conservation of energy :

(KE+PE)₁ (downhill) = (KE+PE)₂ (up the hill)

PE₁=0⇒h=0

KE₂=0⇒v=0(stop), so equation becomes :

KE₁=PE₂

$\tt KE_1=3070.625\\\\KE_1=mgh_2\\\\3070.625=85\times 9.8\times h\Rightarrow h=3.686~m$