Problem 26.5 Sunlight enters a room at an angle of 32 ? above the horizontal and

Question

Problem 26.5

Sunlight enters a room at an angle of 32 ? above the horizontal and reflects from a small mirror lying flat on the floor. The reflected light forms a spot on a wall that is 2.0 m behind the mirror, as shown in the figure(Figure 1).

Part A

If you now place a pencil under the edge of the mirror nearer the wall, tilting it upward by 5.0 ? , how much higher on the wall (?y) is the spot?

Express your answer as a whole number.

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Figure 1 of 1

Problem 26.5

Sunlight enters a room at an angle of 32 ? above the horizontal and reflects from a small mirror lying flat on the floor. The reflected light forms a spot on a wall that is 2.0 m behind the mirror, as shown in the figure(Figure 1).

Part A

If you now place a pencil under the edge of the mirror nearer the wall, tilting it upward by 5.0 ? , how much higher on the wall (?y) is the spot?

Express your answer as a whole number.

SubmitMy AnswersGive Up

Incorrect; Try Again; 4 attempts remaining; no points deducted

Provide FeedbackContinue

Figure 1 of 1

Explanation / Answer

In first condition a right triangle is formed with angle 32 & base 2.0 m.
If the hypotenuse is y,it will be height of the spot on the wall in this condition.
tan32 = y / 2.0 (1)
y = 2.0 * tan32 = 2.0*0.62 = 1.24
in the second condition,
tan37 = y'/2.0 (approx)(2)
y' = 2.2 * tan37 = 2.0 * .75 = 1.50
From (1) & (2),

So y' - y = 1.50 - 1.24= 0.26m = 26cm
That's the approx ans since we have not considered the actual length of the y'. it should be some what smaller than the value obtained as the mirror is tilted upwards so the perpendicular in the triangle will be somewhat smaller.

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