A 22 cm diameter bowling ball has a terminal speed of 85 m/s. What is the ball's mass?

Vterminal=square root of (4mg/pa)

p=1.22(density of air)
a=22cm=.22m/2=.11m(radius)... (pi)r^2=.038=a
85^2 = 4mg/pa
7225 = 4(m)(9.8)/(1.22)(.038)
7225(.038)(1.220)/(4)(9.8) = m
8.54kg=m

Vterminal=square root of (4mg/pa)

p=1.22(density of air)
a=22cm=.22m/2=.11m(radius)... (pi)r^2=.038=a
85^2 = 4mg/pa
7225 = 4(m)(9.8)/(1.22)(.038)
7225(.038)(1.220)/(4)(9.8) = m
8.54kg=m

Vterminal=square root of (4mg/pa)

p=1.22(density of air)
a=22cm=.22m/2=.11m(radius)... (pi)r^2=.038=a
85^2 = 4mg/pa
7225 = 4(m)(9.8)/(1.22)(.038)
7225(.038)(1.220)/(4)(9.8) = m
8.54kg=m

Why did the bowling ball go to the gym? Because it wanted to increase its terminal speed!

To determine the mass of the bowling ball, we can use the formula for terminal speed which relates mass, gravitational force, drag force, and cross-sectional area. The formula is given by:

v_terminal = sqrt((2 * m * g) / (ρ * A * C))

where:
- v_terminal is the terminal speed
- m is the mass of the bowling ball
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- ρ (rho) is the density of the fluid (in this case, air)
- A is the cross-sectional area of the bowling ball
- C is the drag coefficient

In this case, we are given the diameter of the bowling ball, so we need to calculate the cross-sectional area using the formula for the area of a circle:

A = π * r^2

where:
- A is the cross-sectional area
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the bowling ball, which is half of the diameter

Given the diameter of 22 cm, we can first calculate the radius:

r = 22 cm / 2 = 11 cm = 0.11 m

Now, we can calculate the cross-sectional area:

A = π * (0.11 m)^2

Next, we need to know the density of air, which is approximately 1.2 kg/m^3. The drag coefficient for a smooth sphere is typically around 0.47.

Now, we can rearrange the formula for terminal speed and solve for the mass of the bowling ball:

m = (v_terminal^2 * ρ * A * C) / (2 * g)

Substituting the given values, we have:

m = (85 m/s)^2 * (1.2 kg/m^3) * (π * (0.11 m)^2) * 0.47 / (2 * 9.8 m/s^2)

Evaluating the expression, we can find the mass of the bowling ball.