A speedboat travels in a straight line and increases in speed uniformly from υ i = 20.0 m/s to υ f = 30.0 m/s in displacement Δ x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υ i , υ f , and Δ x . (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
A speedboat travels in a straight line and increases in speed uniformly from υ i = 20.0 m/s to υ f = 30.0 m/s in displacement Δ x of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υ i , υ f , and Δ x . (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
Solution Summary: The author explains that the coordinate system for the given situation is used to show the position of the points on the axis.
A speedboat travels in a straight line and increases in speed uniformly from υi = 20.0 m/s to υf = 30.0 m/s in displacement Δx of 200 m. We wish to find the time interval required for the boat to move through this displacement, (a) Draw a coordinate system for this situation, (b) What analysis model is most appropriate for describing this situation? (c) From the analysis model, what equation is most appropriate for finding the acceleration of the speedboat? (d) Solve the equation selected in part (c) symbolically for the boats acceleration in terms of υi, υf, and Δx. (e) Substitute numerical values lo obtain the acceleration numerically. (f) Find the time interval mentioned above.
Taking a Hike
A hiker begins a trip by first walking 21.0 km southeast from her car. She stops and sets up her tent for the night. On the second day, she walks 46.0 km in a direction 60.0° north of east, at which point she discovers a forest ranger's tower.
y (km)
Can
N
W-DE
45.0°
60.0°
Tent
Tower
B
x (km)
☹
(a) Determine the components of the hiker's displacement for each day.
SOLUTION
Conceptualize We conceptualize the problem by drawing a sketch as in the figure. If we denote the displacement vectors on the first and second days by A and B, respectively, and use the ---Select-- as the origin of coordinates, we obtain the vectors shown in the figure. The sketch allows us to estimate the resultant vector as shown.
Categorize Drawing the resultant R, we can now categorize this problem as one we've solved before: --Select-- of two vectors. You should now have a hint of the power of categorization in that many new problems are very similar to problems we have already solved if we are…
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You want to determine if a new material created for solar panels increases the amount of energy that can be captured . You have acquired 15 panels of different sizes manufactured with different materials including the new material.You decide to set up an experiment to solve this problem .What do you think are the 3 most important variables to address in your experience? How would you incorporate those materials in your experiment?
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