A block at t=0 is at the bottom of the plane and is projected up an inclined plane with initial speed v0. The plane's acute angle is θ above the horizontal, and the coefficient of friction is μ between the block and plane.
Find the time (t) and velocity (v1) of the block when it reaches a given distance d.
2. d=(1/2)at^2 + v0t + d0
The Attempt at a Solution
I drew a picture electronically:
I made the direction FN and v0 positive.
F = ma
F = -FμN - mgsinθ
ma = -μmgcosθ - mgsinθ
a = g(-μcosθ - sinθ)
So I found my a (should be a negative value), and now I want to find t when the block reaches d.
d = (1/2)(-at^2) +v0t +d0
0 = (1/2)(-at^2) +v0t + 0 - d
Problem: Acceleration and distance are negative so the roots are imaginary, but I need to find real roots of t and then plug it in v1=at+v0 (I think).