Physic problem(2)...Please help
posted by pyhsiclover on .
A 15 kg, 1 m wide door which has frictionless hinges is closed but unlocked. A 400 g ball hits the exact middle of the door at a velocity of 35 m/s and bounces off elastically, thereby causing the door to slowly swing open. How long in seconds does it take for the door to fully open (rotate 90 degrees)?

1.68?

no. wrong answer

In vector form:
Δp⃗ =p₂⃗p₁⃗ =mv₂⃗mv₁⃗,
for magnitudes
Δp =p₂(p₁) =mv₂+mv₁= 2mv.
p=Mu =>
Mu=2mv
The speed of the center of the door is
u=2mv/M=2•0.4•35/15 = 1.37 m/s
Its angular speed is
ω=u/r=2u/L =2. •1.87/1 = 3.73 rad/s
t= φ/ ω =π/3.73 = 0.84 s. 
wrong answer Elena

0.43 s