2. (2 points) Free falling mass inside a gravity field with air resistance (-bv). A ball of mass m = 2 kg is kicked vertically upwards from the Earth's ground with an initial speed vo = 39.24 m/s. Now we model the air's resistance as Fa = -bu, where b = 0.02 N-¹m/s and v(t) the ball's velocity. - Define a suitable 1-D coordinate system, Ox (provide a sketch) and use the Newton's 2nd law to find the ball's position as a function of time. The ball reaches its maximum height h₁ at time t₁ and hits the ground at time t₂ with velocity v2. (2.1) Find t₁. (2.2) Find v₂. - also consider to find h1, t2 (Hint: you may assume that at this time (t₂) we have bt₂/m << 1 and use the Taylor approximation formula up to third term eªª ≈ 1 + ax + a²x²/2 to simplify the resulting formulas)

2. (2 points) Free falling mass inside a gravity field with air resistance (-bv). A ball of mass m = 2 kg is kicked vertically upwards from the Earth's ground with an initial speed vo = 39.24 m/s. Now we model the air's resistance as Fa = -bu, where b = 0.02 N-¹m/s and v(t) the ball's velocity. - Define a suitable 1-D coordinate system, Ox (provide a sketch) and use the Newton's 2nd law to find the ball's position as a function of time. The ball reaches its maximum height h₁ at time t₁ and hits the ground at time t₂ with velocity v2. (2.1) Find t₁. (2.2) Find v₂. - also consider to find h1, t2 (Hint: you may assume that at this time (t₂) we have bt₂/m << 1 and use the Taylor approximation formula up to third term eªª ≈ 1 + ax + a²x²/2 to simplify the resulting formulas)