Q: A football is kicked with a velocity of 8.5 m/s at an angle of 350 with respect to the football field:
At the moment of takeoff, the football has a vertical component of motion of 4.9 m/s. What is the horizontal component of motion?
A: Since an angle and a diagonal vector have been provided, we may use trigonometry to solve the problem; however, since a vector and one of its components have been given to us, the Pythagorean Theorem would suffice as well. Let’s first choose an appropriate trigonometric function to solve the problem:
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adj
The horizontal ( adj ) component of motion is what we want, so the cos θ function will give us the answer we seek:
cos 350 = adj/( 8.5 m/s )
( 8.5 m/s )( cos 350 ) = adj
( 8.5 m/s )( 0.82 ) = 7.0 m/s
The Pythagorean Theorem relates the sides of a right triangle without reference to the angle between the adjacent side and hypotenuse:
a2 + b2 = c2
Appropriate substitution yields the following results:
?2 + ( 4.9 m/s )2 = ( 8.5 m/s )2
?2 + 24 m2/s2 = 72 m2/s2
?2 = 72 m2/s2 – 24 m2/s2
?2 = 48 m2/s2
? = 6.9 m/s
RENAISSANCE PHYSICS 