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)
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![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3ffb7ae-8f5c-44b2-8d1e-e3b3b64d1aff%2F03f5e442-b3bf-4cb6-92b6-6e8ef2d76d6d%2Fy4ez6hl_processed.png&w=3840&q=75)
Transcribed Image Text: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)
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