A fan cart initially has an acceleration of 1.6m/s/s when it's fan is directed straight backwards. If you rotate the fan by 45°, by what percentage do you expect the fan cart's thrust to decrease? (Answer should be in units of %)

A Fan Cart Initially Has An Acceleration Of 1.6m/s/s When It's Fan Is Directed Straight Backwards. If You Rotate The Fan By 45o, By What Percentage Do You Expect The Fan Cart's Thrust To Decrease? (Answer Should Be In Units Of 96)

a. 45%

b. 29%

c. 71%

d. 50%

The correct answer is d.

d. 50%

Explanation:

Fan cart acceleration = 1.6 m/s²

Thrust = 0.25*π*D²*ρ*v*Δv

where Δv = acceleration component and all factors remaining cconstant, when the fan is rotated by 45 ° the diameter changes to D₂ = sin 45 * D

or 0.707*D. The thrust becomes 0.25*π * (0.707*D) ²*ρ*v*Δv

=0.25*π*0.5*D²*ρ*v*Δv or 0.5 (0.25*π*D²*ρ*v*Δv)

That is the thrust reduces by 50 %