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Question 3
A ship travels from
P to
Q on a course of
060^(@) for
25km and then from
Q to
R on a course of
015^(@) for
30km. How far east of
P is
R, correct to 2 decimal places?
A
29.41km
B
41.29km
C
29.42km
D
41.48km
E
51.34km

Question $3$ $\newline$ A ship travels from $\mathrm{P}$ to $\mathrm{Q}$ on a course of $060^{\circ}$ for $25 \mathrm{~km}$ and then from $\mathrm{Q}$ to $\mathrm{R}$ on a course of $015^{\circ}$ for $30 \mathrm{~km}$ . How far east of $P$ is $R$ , correct to $2$ decimal places? $\newline$ A $\mathrm{Q}$ $0$ $\newline$ B $\mathrm{Q}$ $1$ $\newline$ C $\mathrm{Q}$ $2$ $\newline$ D $\mathrm{Q}$ $3$ $\newline$ E $\mathrm{Q}$ $4$

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Math Problems

Grade 8

Translations: find the coordinates

Full solution

Q. Question

3

\newline

A ship travels from

\mathrm{P}

\mathrm{Q}

on a course of

060^{\circ}

for

25 \mathrm{~km}

and then from

\mathrm{Q}

\mathrm{R}

on a course of

015^{\circ}

for

30 \mathrm{~km}

. How far east of

P

R

, correct to

2

decimal places?

\newline

\mathrm{Q}

0

\newline

\mathrm{Q}

1

\newline

\mathrm{Q}

2

\newline

\mathrm{Q}

3

\newline

\mathrm{Q}

4

Question Prompt: Question prompt: How far east of $P$ is $R$ after the ship travels from $P$ to $Q$ and then from $Q$ to $R$ ?
Calculate Eastward Distance P to Q: The ship travels from P to Q at a course of $060$ degrees for $25$ km. This means it's moving northeast. To find the eastward distance, we calculate the horizontal component using cosine. $ext{Cos}(60) imes 25$ km.
Calculate Eastward Distance Q to R: Calculate the eastward distance from P to Q: $\cos(60) \times 25 = 0.5 \times 25 = 12.5 \, \text{km}.$
Add Eastward Distances: The ship then travels from Q to R at a course of $015$ degrees for $30$ km. This is closer to due north, but still has an eastward component. We calculate this using cosine again. $\cos(15) \times 30$ km.
Add Eastward Distances: The ship then travels from Q to R at a course of $015$ degrees for $30$ km. This is closer to due north, but still has an eastward component. We calculate this using cosine again. $\cos(15) \times 30$ km. Calculate the eastward distance from Q to R: $\cos(15) \times 30 \approx 0.9659 \times 30 \approx 28.98$ km.
Add Eastward Distances: The ship then travels from Q to R at a course of $015$ degrees for $30$ km. This is closer to due north, but still has an eastward component. We calculate this using cosine again. $\cos(15) \times 30$ km. Calculate the eastward distance from Q to R: $\cos(15) \times 30 \approx 0.9659 \times 30 \approx 28.98$ km. Add the eastward distances from P to Q and Q to R to find the total eastward distance from P to R: $12.5$ km + $28.98$ km = $41.48$ km.