3. A box is given an initial speed of 3.0 m/s up an incline where the angle θ =22o. Use the diagram below to define the x-y axes. Assume the original position is on the ground (xo and yo = 0). Ignore friction.

Question

3.	A box is given an initial speed of 3.0 m/s up an incline where the angle θ =22o. Use the diagram below to define the x-y axes. Assume the original position is on the ground (xo and yo = 0). Ignore friction.

a.	How far up the plane (in meters) will the box go?

b.	How much total time (in seconds) elapses (starting at 
time = 0) before the box returns to its original position?

Elena · Answer

KE=PE
mv₀²/2=mgh=mgxsinα
x= v₀²/2gsinα=3²/2•9.8•sin22=1.23 m.
a₁=v₀²/2x =9/2•1.23=3.66 m/s²
Upward
v= v₀-a₁t₁
v=0
t₁=v₀/a₁=3/3.66=0.82 s.
Downward
PE=KE
mgxsinα= mv²/2
=> v=v₀ =>
a₂=a₁
=> t₂=t₁
t=2t₁=2•0.82 =1.64 s