Question

A 92-kg fullback moving south with a speed of 5.8 m/s is tackled by a 110-kg lineman running west with a speed of 3.6 m/s. Assuming momentum conservation, determine the speed and direction of the two players immediately after the tackle. Give the direction as an angle, in degrees, south of west.

Answer 1

Answer:

The speed and direction of the two players immediately after the tackle are 3.3 m/s and 53.4° South of West

Explanation:

given information:

mass of fullback, $m_{x}$ = 92 kg

speed of full back, $v_{x}$ = 5.8 to south

mass of lineman, $m_{y}$ =110 kg

speed of lineman, $v_{y}$ = 3.6

according to conservation energy,

assume that the collision is perfectly inelastic, thus

initial momentum = final momentum

                            $P_{ix}$ = $P_{x}$'

                          m₁v₁ = (m₁+m₂)$v_{x}$'

                             $v_{x}$' = m₁v₁/(m₁+m₂)

                                  = (92) (5.8)/(92+110)

                                  = 2.64 m/s

                            $P_{iy}$ = $P_{y}$'

                         m₂v₂ = (m₁+m₂)$v_{y}$'

                             $v_{y}$' = m₁v₁/(m₁+m₂)

                                  = (110) (3.6)/(92+110)

                                  = 1.96 m/s

thus,

$v$' = √$v_{x}$'²+$v_{y}$'²

  = 3.3 m/s

then, the direction of the two players is

θ = 90 - tan⁻¹($v_{y}$'/$v_{x}$')

  = 90 - tan⁻¹(1.96/2.64)

  = 53.4° South of West