Question

A soccer player with a mass of 60 kg is traveling at 8 m/s when he completes a corner kick on a 0.45 kg soccer ball. The soccer ball travels toward the goal at a speed of 35 m/s. In this elastic collision, what is the speed of the soccer player immediately after kicking the ball?

A) 5.4 m/s
B) 7 m/s
C) 7.7 m/s
D) 8 m/s

Answer 1

v = 7.73 m/s

Step-by-step explanation:

It is given that,

Mass of the player, m₁ = 60 kg

Initial speed of the player, u₁ = 8 m/s

Mass of the soccer ball, m₂ = 0.45 kg

Initial speed of the player, u₂ = 0 (at rest)

After the collision,

Final speed of the player, v₁

Final speed of the ball, v₂ = 35 m/s

Using the conservation of linear momentum to find the final speed of the player. Mathematically, it is given by :

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`m_1u_1=m_1v_1+m_2v_2`

`60* 8=60* v_1+0.45* 35`

`v_1=7.73\ m/s`

So, the speed of the soccer player immediately after kicking the ball is 7.73 m/s. Hence, this is the required solution.

Answer 2

It must be noted that during an elastic collision both the momentum and kinetic energy are conserved. For the kinetic energy, it can be solved through the equation,
KE = 0.5mv²
Equating the kinetic energies before and after collision,
0.5(60)(8 m/s)² = (0.5)(60)(x²) + (0.5)(0.45)(35 m/s)²
The value of x from the equation is approximately 7.40 m/s