Asked by sam
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?
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?
Answers
Answered by
Elena
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
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
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