Question

The largest hailstone every measured fell in Vivian, Nebraska in 2010. The circumference of that hailstone was 19 inches. Using the circumference and the information below, answer the following questions. le Kinetic Energy 0.5MassVelocity (Units: Mass -> kg, Velocity > m/s) Density of the ice in the hail stones 29 Jbs/ft The volume of a sphere is (4/3) #x x r3 The fall velocity of a hailstone in still air can be approximated using this equation V -kVd where k-20 if d (the diameter of the stone) is given in centimeters. V will have units of meters per second (m/s) as long as d is in cm. Density - Mass/Volume Assume the hailstone was spherical (it was actually oblate and measured 8 inches across) and in cm- and in feet What was the diameter of the hailstone in inches What was the total volume of the hailstone in cubic inches What was the fall velocity of this hailstone in m/s What was the total mass of the hailstone in kg What was the total kinetic energy of this hailstone? and cubic feet and in mph and lbs

Answer 1

Answer:

6.04788 in

$115.82654\ in^3$

78.38779 m/s

0.88159 kg

34.55294 J

Explanation:

Circumference is given by

$c=2\pi r\\\Rightarrow r=\dfrac{c}{2\pi}\\\Rightarrow r=\dfrac{19}{2\pi}\\\Rightarrow r=3.02394\ in$

Diameter is given by

$d=2r\\\Rightarrow d=2\times 3.02394\\\Rightarrow d=6.04788\ in$

The diameter is 6.04788 in

$6.04788\times 2.54=15.3616152\ cm$

Volume of sphere is given by

$v=\dfrac{4}{3}\pi r^3\\\Rightarrow v=\dfrac{4}{3}\pi 3.02394^3\\\Rightarrow v=115.82654\ in^3$

The volume is $115.82654\ in^3$

$115.82654\times \dfrac{1}{1728}=0.06702\ ft^3$

Fall velocity is given by

$V=k\sqrt{d}\\\Rightarrow V=20\sqrt{15.3616152}\\\Rightarrow V=78.38779\ m/s$

The velocity of the fall will be 78.38779 m/s

Mass is given by

$m=\rho v\\\Rightarrow m=29\times 0.06702\\\Rightarrow m=1.94358\ lb$

$1.94358\ lb=1.94358\times \dfrac{1}{2.20462}=0.88159\ kg$

The mass is 0.88159 kg

Kinetic energy is given by

$K=\dfrac{1}{2}mv^2\\\Rightarrow K=\dfrac{1}{2}0.88159\times 78.38779\\\Rightarrow K=34.55294\ J$

The kinetic energy is 34.55294 J