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A 250 g ball is launched with a speed of 35 m/s at a 30° angle. A strong headwind exerts a constant horizontal drag force on the ball. What is the magnitude of the drag force if the wind reduces the ball’s travel distance by 20%?

User Amina
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1 Answer

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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

User SlopTonio
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