Radical Equations

A)    r  = 1.80 √ [m / v^2]

7  = 1.80 √ [80 / v^2]        divide both sides by 1.80

7 / 1.80  = √ [80 / v^2]        square both sides

[ 7 / 1.80]^2  = 80/v^2        rearrange as

v^2  =  80 / [ 7 / 1.80]^2      take the square root of both sides

v = √80 / [ 7 / 1.80]   = about 2.3 m/s

B)  9 = 1.80  √ [m /2^2]     divide both sides by 1.80   and simplify inside the root

5 = √ [m / 4]      square both sides

25  = m / 4       multiply both sides by 4

100 = m  = 100 kg

A company that produces parachutes usus a formula r=1.80sqrt(m/v^2) to determine the desenct velocity v (m/s) of an object having a mass m (kg) where r (m) represents the radius of the parachute.

Can you please show steps if at all possible?

A. what is the velocity of an object with mass of 80kg if the parachute has radius of 7m.

B. a safe decent velocity is no more than 2m/s, if a parachute had radius 9m, what is the maximum mass of the object being dropped. 

A) r=1.80sqrt(m/v^2)

7 =1.8 sqrt(80/v^2)

Solve for v:
7=16.0997 sqrt(1/v^2)

7=16.0997 sqrt(1/v^2) is equivalent to 16.0997 sqrt(1/v^2)=7:
16.0997 sqrt(1/v^2)=7

Divide both sides by 16.0997:
sqrt(1/v^2)=0.434791

Raise both sides to the power of two:
1/v^2=0.189043

Take the reciprocal of both sides:
v^2=5.2898

Take the square root of both sides:
Answer: |  v=2.29996 or v=-2.29996

B)

r=1.80sqrt(m/v^2)

9=1.8sqrt(m/2^2)

Solve for m:
9=0.9 sqrt(m)

0.9 sqrt(m)=(9 sqrt(m))/10:
9=(9 sqrt(m))/10

9=(9 sqrt(m))/10 is equivalent to (9 sqrt(m))/10=9:
(9 sqrt(m))/10=9

Multiply both sides by 10/9:
sqrt(m)=10

Raise both sides to the power of two:
Answer: |  m=100