Question

Part D: Application [12 marks] 1. A student is flying their kite and its string is 25m long. As the kite is in the air, it makes an angle of $\frac{\pi}{4}$ with respect to the ground. The wind suddenly changes the position of the kite so that it flies higher and makes and angle of $\frac{\pi}{3}$ with the ground. As well, the sun is directly above and makes a shadow of the kite on the ground. a. Determine the horizontal distance from the student to the end of the shadow for both angles. Must use exact values! b. Determine the distance between the two shadowed locations. 2. An analog watchshows a time of 7 o'clock. What is the exact radian measure of the angle between the hour hand and the minute hand? from the hour hand to the minute hand in clockwise motion

          Part D: Application [12 marks]
1. A student is flying their kite and its string is 25m long. As the kite is in the air, it makes an angle of $\frac{\pi}{4}$ with
respect to the ground. The wind suddenly changes the position of the kite so that it flies higher and makes and
angle of $\frac{\pi}{3}$ with the ground. As well, the sun is directly above and makes a shadow of the kite on the ground.
a. Determine the horizontal distance from the student to the end of the shadow for both angles. Must use exact
values!
b. Determine the distance between the two shadowed locations.
2. An analog watchshows a time of 7 o'clock. What is the exact radian measure of the angle between the hour hand
and the minute hand? from the hour hand to the minute hand in clockwise motion

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Part D: Application [12 marks]
1. A student is flying their kite and its string is 25m long. As the kite is in the air, it makes an angle of (π)/(4) with
respect to the ground. The wind suddenly changes the position of the kite so that it flies higher and makes and
angle of (π)/(3) with the ground. As well, the sun is directly above and makes a shadow of the kite on the ground.
a. Determine the horizontal distance from the student to the end of the shadow for both angles. Must use exact
values!
b. Determine the distance between the two shadowed locations.
2. An analog watchshows a time of 7 o'clock. What is the exact radian measure of the angle between the hour hand
and the minute hand? from the hour hand to the minute hand in clockwise motion

Added by Martin Y.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Craig West

10/18/2022

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We can use the tangent function to find this distance. Show more…

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Part D: Application [12 marks] IT I. A student is flying their kite and its string is 25m long. As the kite is in the air, it makes an angle of 4° with respect to the ground. The wind suddenly changes the position of the kite so that it flies higher and makes an angle of 3° with the ground. As well, the sun is directly above and makes a shadow of the kite on the ground. a. Determine the horizontal distance from the student to the end of the shadow for both angles. Must use exact values! [VV] b. Determine the distance between the two shadowed locations. IVVI 2. An analog watch shows a time of 7 o'clock. What is the exact radian measure of the angle between the hour hand and the minute hand? from the hour hand to the minute hand in clockwise motion [VVV]

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Transcript

00:01 Question, we're told that a kite is gliding horizontally at 30 meters per second while string is let out.

00:06 And then the angle between the string and the horizontal is diminishing.

00:12 So let's go ahead and give that a sketch.

00:20 So here is 30 meters high.

00:24 The kite is going along in this direction.

00:27 This is our x.

00:30 Here is our kite.

00:34 And when the string, we want to know when this angle here, theta we have this angle theta that is diminishing we want to know the rate of change at which the angle diminishes when 60 meters of stringer out and we're told that also told that this kite is gliding this way at three three meters per second okay so that's going to be my dx dt and we want the theta dt when 60 meters of string.

01:44 All right.

01:44 And if there's 60 meters of string, we can just kind of look at here real quick.

01:47 We can try to figure this out.

01:49 So we have x squared plus 30 squared equals 60 squared.

01:56 So x is going to be the square root of 60 squared minus 30 squared, which is 2 ,700.

02:07 And hopefully we recognize that at least 100 is a perfect square, but there's also a factor of nine also.

02:14 So this is 900 times 3, which is 30 times a square to 3.

02:22 Okay, 30 times a square to 3.

02:26 So we need to write an equation that relates x and theta.

02:31 So if theta is an angle here, and with respect to theta, we have the opposite and the adjacent side...

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