The magnitude of the drag force if the wind reduces the ball’s travel distance by 20% is 7.07 N.
How to calculate the drag force?
The magnitude of the drag force if the wind reduces the ball’s travel distance by 20% is calculated as follows.
The maximum horizontal distance traveled without air resistance;
R = (u² sin (2θ) ) / g
where;
- u is the initial velocity of the ball
- g is acceleration due to gravity
- θ is the angle of projection
R = (35² x sin(2 x 30) ) / 9.8
R = 108.25 m
Applying work energy theorem;
change in kinetic energy of ball = work done by friction
¹/₂mv² = Fd
¹/₂mv² = F( x 20% of R)
¹/₂mv² = F(0.2R)
¹/₂mv² = 0.2FR
where;
- F is the drag force
- R is the range
F = (mv²) / (0.2R x 2)
F = (0.25 x 35²) / ( 0.2 x 108.25 x 2)
F = 7.07 N