Question

a football player runs directly down to the field for 26m before turning to the right at an angle of 22 degrees from his original direction and running an additional 20 m before being tackled. what is the magnitude of the runners total displacement and at what angle to his original displacement is his total displacement ( with counterclock-wise positive) answer in units of degrees

Answer 1

let d₁ = 26m and d₂ = 20m. given angle is 22.⁰

the magnitude of the total displacement is d = d₁² + d₂² + 2d₁d₂ cos

            = 26² + 20² + 2x26 x20 cos22⁰ = 45.121m

teh angle is = Tan^-1 ( d₂ sin / ( d₁ + d₂ Cos) = 20 sin22⁰ / ( 26 + 20 Cos 22⁰ )

                                   = Tan ( 0.168)       = 9.37⁰