In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.0342 s, during which time it experiences an acceleration of 186 m/s2. The ball is launched at an angle of 45.9 ° above the ground. Determine the (a) horizontal and (b) vertical components of the launch velocity.

b)      v_y = 4.57 m / s

a)      vₓ = 4.43 m / s

Explanation:

This is an exercise in kinematics, where we assume that the acceleration is in the direction of the force and the initial body with zero velocity

          v = v₀ + a t

          v = 0 + a t

          v = 186  0.0342

          v = 6.36 m / s

let's use trigonometry to decompose this velocity

           sin 45.9 = v_y / v

           cos 45.9 = vₓ / v

           v_y = v sin 45.9

           vₓ = v cos 45.9

           v_y = 6.36 sin 45.9

           vₓ = 6.36 cos 45.9

           v_y = 4.57 m / s

           vₓ = 4.43 m / s

ₓ

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