Question

Problem 1: A shoreline observation post is located on a ciff such that the observer is 310 feet above sea level. Wher initially spotted, the angle of depression (the angle at which an observer needs to look down) from the observation post to an approaching ship was 4.8 a) Draw a diagram of the situation and label each known and unknown quantity measure. b) How far out to sea was the ship when it was first spotted? c) After watching the ship for 47 seconds, the angel of depression was 5.9 Assuming the ship was moving at a constant rate, estimate the ship's velocity. If the ship were to continue on its course at the same velocity, how much time f elapse before the ship crashes into the shore? d) rom the second reading will 29 MacBook Air 80 Fs 6 8

Answer 1

a) A shoreline observation post is located on a cliff such that the observer is 310ft above sea level. When initially spotted, the angle of depression (the angle at which an observer needs to look down) from the observation post to an approaching ship was 4.8 ship cliff AE ос- 310ft 4.80 sea level The figure is shown in the right.

b) How far out to sea was the ship when it was first spotted? cliff 4.80 310ft 4.80 ship sea level In the triangle SOC, tan 43° OC 310 os 0S As tan 4.80 0.084, so 310 OS3690.476ft 0.084

c) After watching the ship for 47 seconds, the angle of depression was 5.9°. Assuming the ship was moving at a constant rate, estimate the ship's velocity the angle of depression was 5.9°, so the distance of the ship from the cliff, is 310 3009.709ft tan 5.9° The ship moves (3690.476ft -3009.709ft) 680.767ft in 47 seconds, and thus 680.767 ship's velocity = 14.484 ft/sec 47 d) If the ship were to continue on its course at the same velocity how much time from the second reading will elapse before the ship crashes into the shore? ft Ans. As velocity is 14.484 take to cover 3009.709ft distance it will sec 3009.709ft_20779 sec 14.484 It sec