A force(F) acting on an object varies jointly as its surface area(A) and the square of its velocity(v). Suppose that a force of 1656 Newtons acts on an object of surface area 0.4 square

Question

A force(F) acting on an object varies jointly as its surface area(A) and

the square of its velocity(v). Suppose that a force of 1656 Newtons

acts on an object of surface area 0.4 square meters when moving at 3

meters per second.

(a) Write a variation equation to represent this relationship. Use k

for the variation constant.

(b) Determine the value of k.

(c) Determine the velocity of an object with surface area 0.25m2 when

a force of 3680 Newtons is acting on it.

Answer 1

F = kAv²

1656 = k(.4)3²

k = 73.6

F=73.6Av²

3680 = 73.6(.25)r²

r² = 200

r = 10√2 = 14.14 m/s