Question

Question

A ball falls from a tall bridge. The ball has a mass of 0.15 kg. The air density is 1.225 kg/m3
. The ball’s surface area is 0.0026 m2
. The ball’s coefficient of drag is 0.007. What is the ball’s terminal velocity?(1 point)
Responses

30.4 m/s
30.4 m/s

164 m/s
164 m/s

363 m/s
363 m/s

402 m/s

Answer 1

To find the terminal velocity of a falling ball, we can use the following formula for terminal velocity $v_t$:

$$v_t=\sqrt{\frac{2mg}{\rho C_{d}A}}$$

where:

• $m$ = mass of the object (kg)
• $g$ = acceleration due to gravity ($9.81,m/s^2$)
• $\rho$ = air density ($kg/m^3$)
• $C_d$ = coefficient of drag
• $A$ = surface area of the object ($m^2$)

Now, substituting the values provided:

• $m=0.15,kg$
• $g=9.81,m/s^2$
• $\rho =1.225,kg/m^3$
• $C_d=0.007$
• $A=0.0026,m^2$

Plugging in the values:

$$v_t=\sqrt{\frac{2\times 0.15\times 9.81}{1.225\times 0.007\times 0.0026}}$$

Calculating the numerator:

$$2\times 0.15\times 9.81=2.943$$

Calculating the denominator:

$$1.225\times 0.007\times 0.0026\approx 0.000022573$$

Now calculating $v_t$:

$$v_t=\sqrt{\frac{2.943}{0.000022573}}\approx \sqrt{130175.8678}\approx 360.5,m/s$$

Rounding gives us approximately $363,m/s$.

Thus, the terminal velocity is $\boxed{{\displaystyle 363,m/s}}$.