A truck on a slope?

Question

Assume that a truck, initially traveling at 45 mph, loses its braking as it travels down a 5% grade (5 feet down for every 100 feet of horizontal travel). Ignoring friction, calculate the maximum speed possible after the trunk has moved 2 miles down the slope after the clutch went out.

How do I set this up? Thanks.

Answer 1

Break and clutch failure! WOW!

Kinetic energy at the bottom = potential energy at the top

Ke=Pe
Ke= 0.5 m V^2
Pe= mgh

for a 2 mi path S=2 x 5280= 10560 ft
h= S sin(A)
A=arcTan(5/100)

Now
0.5mV^2=mgh
V=sqrt(2gh)
Vf= V+ 45mph

When calculating keep units in mind