If the pilot was forced to reduce the plane's speed to 150km/h, how much would she need to increase the angle at which the plane is pointing (relative to north) in order for the plane to continue to travel due north? Answer: 8.7°
If the pilot was forced to reduce the plane's speed to 150km/h, how much would she need to increase the angle at which the plane is pointing (relative to north) in order for the plane to continue to travel due north? Answer: 8.7°
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Only practice problem 3.11.
The second photo has background info to help solve the problem.
![**Example 3.1: Compensating for a Crosswind**
**Set Up:**
Now, the information given is:
- \(\vec{v}_{PG} = 240 \, \text{km/h}\), the direction unknown.
- \(\vec{v}_{PA} = 100 \, \text{km/h}\).
**Solve:**
We aim to find \(\beta\), the angle the plane must head towards the north in order to compensate for the crosswind and maintain its velocity relative to the ground, \(\vec{v}_{PG}\). The velocity of the plane relative to the air, \(\vec{v}_{PA}\), is at a right angle to \(\vec{v}_{PG}\). Using trigonometry and vector addition methods, resolve the vectors into components and use the equations to solve for \(\beta\).
The three relative velocities must satisfy the vector equation:
\[
\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}
\]
We find that:
\[
\beta = \sin^{-1}\left(\frac{100 \, \text{km/h}}{240 \, \text{km/h}}\right) = 25^\circ
\]
\[
v_{PG} = \sqrt{(240 \, \text{km/h})^2 - (100 \, \text{km/h})^2} = 218 \, \text{km/h}
\]
The pilot should head \(25^\circ\) west of north; her ground speed will then be 218 km/h.
**Reflect:**
When a plane flies in a crosswind that is at right angles to the plane's velocity relative to the ground, its speed relative to the ground is decreased, the trip takes longer than in calm air.
**Practice Problem:**
If the plane maintains its speed of 240 km/h, but the crosswind is 75 km/h, how much would she need to increase the plane’s speed relative to the ground in order for the plane to continue to travel due north? (Answer: 8°).
**Diagram Explanation:**
- **Figure 3.22:** Shows a vector diagram with the plane's velocity vectors. The plane uses orientation to travel due north. The longest vector indicates the airspeed, a second vector represents the crosswind, and the resultant vector shows the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28764828-4d1c-44b8-9544-7d79c8b69e6b%2F0918fe06-d6af-494b-8200-9d528346e5fb%2F0egyzu5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 3.1: Compensating for a Crosswind**
**Set Up:**
Now, the information given is:
- \(\vec{v}_{PG} = 240 \, \text{km/h}\), the direction unknown.
- \(\vec{v}_{PA} = 100 \, \text{km/h}\).
**Solve:**
We aim to find \(\beta\), the angle the plane must head towards the north in order to compensate for the crosswind and maintain its velocity relative to the ground, \(\vec{v}_{PG}\). The velocity of the plane relative to the air, \(\vec{v}_{PA}\), is at a right angle to \(\vec{v}_{PG}\). Using trigonometry and vector addition methods, resolve the vectors into components and use the equations to solve for \(\beta\).
The three relative velocities must satisfy the vector equation:
\[
\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}
\]
We find that:
\[
\beta = \sin^{-1}\left(\frac{100 \, \text{km/h}}{240 \, \text{km/h}}\right) = 25^\circ
\]
\[
v_{PG} = \sqrt{(240 \, \text{km/h})^2 - (100 \, \text{km/h})^2} = 218 \, \text{km/h}
\]
The pilot should head \(25^\circ\) west of north; her ground speed will then be 218 km/h.
**Reflect:**
When a plane flies in a crosswind that is at right angles to the plane's velocity relative to the ground, its speed relative to the ground is decreased, the trip takes longer than in calm air.
**Practice Problem:**
If the plane maintains its speed of 240 km/h, but the crosswind is 75 km/h, how much would she need to increase the plane’s speed relative to the ground in order for the plane to continue to travel due north? (Answer: 8°).
**Diagram Explanation:**
- **Figure 3.22:** Shows a vector diagram with the plane's velocity vectors. The plane uses orientation to travel due north. The longest vector indicates the airspeed, a second vector represents the crosswind, and the resultant vector shows the
Transcribed Image Text:**Page 76 – Practice Problem 3.6**
If the kicker gives the ball the same initial speed and angle but the ball is kicked from a point 25m from the goalpost, what is the height of the ball above the crossbar as it crosses over the goalpost?
**Answer:** 1.2m.
**Page 77 – Practice Problem 3.7**
Suppose the pear is released from a height of 6.00m above the archer’s arrow, the arrow is shot at a speed of 30.0m/s, and the distance between the archer and the base of the tower is 15.0m. Find the time at which the arrow hits the pear, the distance the pear has fallen, and the height of the arrow above its release point.
**Answers:** 0.54s, 1.4m, 4.6m.
**Page 80 – Practice Problem 3.8**
A more reasonable maximum acceleration for varying pavement conditions is 5.0m/s². Under these conditions, what is the maximum speed at which a car can negotiate a flat curve with radius 230m?
**Answer:** 34m/s = 76mi/h.
**Page 81 – Practice Problem 3.9**
If the ride increases in speed so that T = 2.0s, what is a_rad? (This question can be answered by using proportional reasoning, without much arithmetic.)
**Answer:** 49 m/s².
**Page 83 – Practice Problem 3.10**
If the plane has an airspeed of 240km/h, but the wind decreases, what is the wind speed if the plane’s velocity with respect to earth is 15° east of north?
**Answer:** 64 km/h.
**Page 84 – Practice Problem 3.11**
If the pilot was forced to reduce the plane’s speed to 150km/h, how much would she need to increase the angle at which the plane is pointing (relative to north) in order for the plane to continue to travel due north?
**Answer:** 8.7°.
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