23. Three points P, Q and R are on level ground. Q is 240 m from P on bearing of 230°. R is 120 m to the east of P.
(a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R in the space provided below.
(b) Determine
(i) The distance R from Q;
(ii) The bearing of R form Q.
(c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at Q to the pot of the post at P. Given that the angle of depression of the top of the post at P from the top of post at Q is 9°, calculate:
(i) The distance to the nearest meter, the bird covers;
(ii) The speed of the bird in km/h
b. All angles are measured CW from +y-axis.
Given: PQ = 240m[230o].
PR = 120m[90o].
QR = ?
PQ + QR = PR.
QR = PR - PQ,
QR = 120[90o] - 240[230o],
QR = (120*sin90+240*sin230) + (120*Cos90+240*Cos230)I,
(i). QR = -63.9 - 154.3i = 167m.[22.5o] W. of S.
(ii). 22.5o W. of S. = 202.5o CW(bearing).
I need workout
another ranch-type question? No ideas yet?
(a) To draw the diagram, we can use a scale of 1 cm to represent 40 m. Draw a point P at the center of the diagram. From point P, draw a line segment 6 cm long at an angle of 230°. Label the endpoint of this line segment as Q. From point P, draw another line segment 3 cm long in the east direction. Label the endpoint of this line segment as R.
(b) (i) To find the distance from Q to R, we can use the Pythagorean theorem. The distance in the east direction is 120 m, and the distance in the north direction is 240 m. Therefore, the distance from Q to R can be found using the formula: distance = sqrt((240^2) + (120^2)). Calculate the value to find the distance.
(ii) To find the bearing of R from Q, we need to determine the angle between the line QR and the north direction. We can use trigonometry to find this angle. The east distance is given as 120 m, and the north distance is given as 240 m. So, the tangent of the angle is equal to the east distance divided by the north distance. Calculate the angle using the inverse tangent function.
(c) (i) To find the distance the bird covers, we can use the concept of right-angled triangles. The angle of depression is given as 9 degrees, which means that the angle between the line PQ and the horizontal ground is also 9 degrees. We can use trigonometry to find the distance covered by the bird. The opposite side of the angle is the height difference between the top of the post at Q and the top of the post at P. Calculate the distance using the formula: distance = opposite side / tangent(angle).
(ii) To find the speed of the bird, we need to convert the distance covered by the bird from meters to kilometers and the time from seconds to hours. Divide the distance by 1000 to convert it to kilometers, and divide the time by 3600 to convert it to hours. Finally, divide the distance (in kilometers) by the time (in hours) to find the speed of the bird in km/h.