1. The problem statement, all variables and given/known data
Last weekend you and a friend were out for a walk on a pleasant spring evening.
The sky was clear and the temperature was 10.0°C. You arrived at the entrance to long
straight automobile tunnel and take out your physics sound recording equipment. You
hope to do some calculations based on the frequencies you record. As you were standing
at the mouth of the tunnel, a black 2012 Toyota Highlander drove by at a constant speed
(which seems near the speed limit.) You also noticed that a child in the passenger seat
had her hand out the window with a glass of water in that hand! Pondering the safety of
the child’s situation, you suddenly hear screeching tires from down the tunnel! The
screech is shortly followed by a loud crash!
You look into the tunnel and the Highlander is just pulling off to the side of the
road obviously damaged. You and your friend run down the tunnel to help but it seems
everyone is ok, just shaken up. You notice that the glass is lying broken and seems to
have landed 2.20m just outside the tunnel. The girl that was holding it comes up beside
you and sees the glass. She says she let go of it when the two cars collided.
You go home and analyze your sound data and find some interesting pieces of evidence:
I. The pitch of the Highlander’s motor coming towards you is 367.2 Hz, while a
typical motor is 343.1 Hz at this approximate speed.
II. You recorded a low frequency from the tunnel, which seems to be its fundamental
resonant frequency, at 240.6 mHz.
III. The screech of the tires started exactly 29.95 seconds after the Highlander passed
you and entered the tunnel.
A week later you discover that the case has gone to court and there are some
details that are under debate. The driver of the Highlander argues that the other car was
actually stopped on his side of the road, inside the tunnel. The other driver states that he
was actually parked outside the tunnel! This driver also argues that the Highlander
driver did not make acceptable effort to slow down before hitting his car.
You decide to approach the police with your sound data to try and help solve the
case. The police agree and share some information with you. The deformation of the cars
in the crash indicate a collision of approximately 38.510 kJ, but the Highlander’s final
velocity has yet to be determined. You remember from your studies of Physics that an
average co-efficient of Friction for car tires on dry asphalt is 0.82. You also do some
research and find the mass of the Highlander to be 2490kg and the window height to be
1.22m. Can you help the police give full evidence of what happened?
A. What was the Highlander’s speed when the collision occurred?
B. Did the Highlander driver apply his breaks at close to full capacity?
C. Was the other car actually inside the tunnel when the collision occurred?
I just dont even know where to start. Any help would be appreciated. Thanks.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Last weekend you and a friend were out for a walk on a pleasant spring evening.
The sky was clear and the temperature was 10.0°C. You arrived at the entrance to long
straight automobile tunnel and take out your physics sound recording equipment. You
hope to do some calculations based on the frequencies you record. As you were standing
at the mouth of the tunnel, a black 2012 Toyota Highlander drove by at a constant speed
(which seems near the speed limit.) You also noticed that a child in the passenger seat
had her hand out the window with a glass of water in that hand! Pondering the safety of
the child’s situation, you suddenly hear screeching tires from down the tunnel! The
screech is shortly followed by a loud crash!
You look into the tunnel and the Highlander is just pulling off to the side of the
road obviously damaged. You and your friend run down the tunnel to help but it seems
everyone is ok, just shaken up. You notice that the glass is lying broken and seems to
have landed 2.20m just outside the tunnel. The girl that was holding it comes up beside
you and sees the glass. She says she let go of it when the two cars collided.
You go home and analyze your sound data and find some interesting pieces of evidence:
I. The pitch of the Highlander’s motor coming towards you is 367.2 Hz, while a
typical motor is 343.1 Hz at this approximate speed.
II. You recorded a low frequency from the tunnel, which seems to be its fundamental
resonant frequency, at 240.6 mHz.
III. The screech of the tires started exactly 29.95 seconds after the Highlander passed
you and entered the tunnel.
A week later you discover that the case has gone to court and there are some
details that are under debate. The driver of the Highlander argues that the other car was
actually stopped on his side of the road, inside the tunnel. The other driver states that he
was actually parked outside the tunnel! This driver also argues that the Highlander
driver did not make acceptable effort to slow down before hitting his car.
You decide to approach the police with your sound data to try and help solve the
case. The police agree and share some information with you. The deformation of the cars
in the crash indicate a collision of approximately 38.510 kJ, but the Highlander’s final
velocity has yet to be determined. You remember from your studies of Physics that an
average co-efficient of Friction for car tires on dry asphalt is 0.82. You also do some
research and find the mass of the Highlander to be 2490kg and the window height to be
1.22m. Can you help the police give full evidence of what happened?
A. What was the Highlander’s speed when the collision occurred?
B. Did the Highlander driver apply his breaks at close to full capacity?
C. Was the other car actually inside the tunnel when the collision occurred?
I just dont even know where to start. Any help would be appreciated. Thanks.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
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