7. A plastic cup, 15.0 cm in height, is filled to the rim with water. A small hole is punctured in the cup at a height 9.00 cm above the bottom of the cup and is allowing water to spew out. At what distance does the water land from the bottom of the cup?(Answer is 14.6 cm)
2 answers
Use bernoulli's equation to find the velocity of the water leaving when the depth is the full cup. From height of the hole (assume vertical free fall), and velocity, calculate horizontal distance.
h=0.15 m, hₒ=0.09 m.
Bernoulli’s equation between the top surface and the exitting stream:
Pₒ+0+ρghₒ=Pₒ+ρv²/2+ ρgh,
v² = 2g(hₒ-h),
v=sqrt{2g(hₒ-h)}=sqrt{2•9.8•(0.15-0.09)} =1.08m/s.
y=h=gt²/2.
t=sqrt(2h/g) =sqrt(2•0.09/9.8)=0.135 s.
x=vt=1.08•0.135=0.146 m = 14.6 cm
Bernoulli’s equation between the top surface and the exitting stream:
Pₒ+0+ρghₒ=Pₒ+ρv²/2+ ρgh,
v² = 2g(hₒ-h),
v=sqrt{2g(hₒ-h)}=sqrt{2•9.8•(0.15-0.09)} =1.08m/s.
y=h=gt²/2.
t=sqrt(2h/g) =sqrt(2•0.09/9.8)=0.135 s.
x=vt=1.08•0.135=0.146 m = 14.6 cm
1 answer