Please give final answers in (cm) Problem 15.100 Part A A tin can is filled with

Question

Please give final answers in (cm)

Problem 15.100 Part A A tin can is filled with water to a depth of 45 cm A hole 14 cm above the bottom of the can produces a stream of water that is directed at an angle of 40° above the horizontal. Find the range of this stream of water. Express your answer using two significant figures. cm Submit My Answers Give Up Incorrect, Try Again; 2 attempts remaining Part B Find the maximum height of this stream of water. Express your answer using two significant figures. Umax cm Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

A)

Use Benoulli to find the speed of the water. Then use projectile kinematics to find the height and range.

P1 + 1/2*density*v1^2 + density*g*h1 = P2 + 1/2*density*v2^2 + density*g*h2

Point 1 is directly across from the hole at the same height in the fluid. Point 2 is right at the hole. We assume the

atmosheric pressure is the same at both locations... P1 = P2 and those cancel.

1/2*dnsity*v1^2 + density*g*h1 = 1/2*density*v2^2 + density*g*h2

The densities are the same, they cancel

1/2*v1^2 + g*h1 = 1/2*v2^ + g*h2

At 1 the fluid is not moving

g*h1 = 1/2*v2^2 + g*h2

At 2, there is no column of fluid above the hole outside of the can, h2 = 0

g*h1 = 1/2*v2^2

Solve for v2

v2 = sqrt(2*g*h1)

where h1 = 45 cm - 14 cm = 31 cm = 0.31 m

v2 = sqrt(2 x 9.81 m/s^2 x 0.31 m)

v2 = 2.466 m/s

Vertical component:

vyi = v2*sin(40) = 1.585 m/s

Horizontal component:

vx = v2*cos(40) = 1.889 m/s

In the vertical direction find the time it take to land:

hf = hi + vyi*t - 1/2*g*t^2

With hf = 0, hi = 0.14 m, solve for t using the quadratic equation

0 = 0.14 + 1.585*t - 4.9*t^2

t = 0.3956 s (the other time was negative)

Range = vx*t = 1.889 m/s * 0.3956 s = 0.7473 m = 74.73 cm

B)

Find the time it takes to get the top. At the top, the vertical velocity is 0.

vf = vyi - g*t

t = vyi/g

t = 1.585 m/s / 9.81 m/s^2

t = 0.16 s

Plug that into the equation of motion:

hf = hi + vyi*t - 1/2*g*t^2

hf = 0.14 m + 1.585 m/s * 0.16 s - 4.9 m/s^2 * (0.16 s)^2

hf = 0.268 m = 26.8 m

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