a loaded window. She fires the suction dart at (a), and the dart sticks on to the window a moment later at (b). The situation as observed from the car's frame is shown below. As you can see, the suction dart flies straight north. Backseat shooting: in car's frame (b) (a) O Backseat shooting: in Earth's frame (a): 0 (b) 1, north north east east But in the Earth's reference frame, the car moves between the firing of the dart and its sticking onto the window. The situation at firing is shown with dashed lines and the situation at sticking is shown with solid lines. As you can see, the dart flies in a direction somewhat east of north. a. If the speed of the car relative to the Earth is the same as the speed of the dart relative to the car, in what direction does the dart travel in the Earth's frame? (North? East? Northeast? Between north and northeast? Between northeast and east?) What if the speed of the car relative to the Earth is less than the speed of the dart relative to the car? b. Argue that the dart travels faster in the Earth's frame than it does in the car's frame.
a loaded window. She fires the suction dart at (a), and the dart sticks on to the window a moment later at (b). The situation as observed from the car's frame is shown below. As you can see, the suction dart flies straight north. Backseat shooting: in car's frame (b) (a) O Backseat shooting: in Earth's frame (a): 0 (b) 1, north north east east But in the Earth's reference frame, the car moves between the firing of the dart and its sticking onto the window. The situation at firing is shown with dashed lines and the situation at sticking is shown with solid lines. As you can see, the dart flies in a direction somewhat east of north. a. If the speed of the car relative to the Earth is the same as the speed of the dart relative to the car, in what direction does the dart travel in the Earth's frame? (North? East? Northeast? Between north and northeast? Between northeast and east?) What if the speed of the car relative to the Earth is less than the speed of the dart relative to the car? b. Argue that the dart travels faster in the Earth's frame than it does in the car's frame.
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Transcribed Image Text:PROBLEMS
2.1+ Backseat shooting. You are driving a car due east down a highway. Your young
daughter is strapped into her child seat in the back, on the south side of the car, holding
a loaded suction dart gun. She decides to shoot a suction dart onto the opposite back
window. She fires the suction dart at (a), and the dart sticks on to the window a moment
later at (b). The situation as observed from the car's frame is shown below. As you can
see, the suction dart flies straight north.
Backseat shooting: in car's frame
(b)
(a) o
Backseat shooting: in Earth's frame
O
(a) O
(b)
north
north
east
east
But in the Earth's reference frame, the car moves between the firing of the dart and its
sticking onto the window. The situation at firing is shown with dashed lines and the
situation at sticking is shown with solid lines. As you can see, the dart flies in a direction
somewhat east of north.
a. If the speed of the car relative to the Earth is the same as the speed of the dart
relative to the car, in what direction does the dart travel in the Earth's frame?
(North? East? Northeast? Between north and northeast? Between northeast and
east?) What if the speed of the car relative to the Earth is less than the speed of
the dart relative to the car?
b. Argue that the dart travels faster in the Earth's frame than it does in the car's
frame.
Expert Solution
Step 1
Here it is given that the speed of the car relative to the Earth is equal to speed of the dart relative to the car.
Let us assume that the dart and car has speed v.
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