P
Princess Kasumi
Guest
1. A helicopter pilot is informed that a lifeboat is drifting in the sea with constant velocity (-2i + 4j) km/h and that, relative to his position, the lifeboat has a position vector (10i + 5j) km. The helicopter is traveling at 100 km/h and the pilot immediately moves to intercept the lifeboat in the shortest possible time. Given that the constant velocity of the helicopter is (ui + vj) km/h. Show that:
(a) u = 2v – 10
(b) v² - 8v – 1980 = 0
(c) Calculate the time taken by the helicopter to reach the lifeboat
(d) Calculate the bearing of the course taken by the helicopter
2. The points A and B have position vectors (30i – 60j) m and (-20i + 60j) m respectively relative to an origin O, where i and j are unit vectors. A cyclist, Chris, starts at A and cycles towards B with constant speed 2.6 m/s. Another cyclist, Doug, starts at O and cycles towards B with constant speed k√10 m/s. Find the value of k.
3. At 11:00 hours the position vector on an aircraft relative to an airport O is (200i – 30j) km, i and j are unit vectors due east and north respectively. The velocity of the aircraft is (180i – 120j) km/h. Find the time when the aircraft is due east of the airport O.
Thanks for answering. Please include steps and explanation as possible.
(a) u = 2v – 10
(b) v² - 8v – 1980 = 0
(c) Calculate the time taken by the helicopter to reach the lifeboat
(d) Calculate the bearing of the course taken by the helicopter
2. The points A and B have position vectors (30i – 60j) m and (-20i + 60j) m respectively relative to an origin O, where i and j are unit vectors. A cyclist, Chris, starts at A and cycles towards B with constant speed 2.6 m/s. Another cyclist, Doug, starts at O and cycles towards B with constant speed k√10 m/s. Find the value of k.
3. At 11:00 hours the position vector on an aircraft relative to an airport O is (200i – 30j) km, i and j are unit vectors due east and north respectively. The velocity of the aircraft is (180i – 120j) km/h. Find the time when the aircraft is due east of the airport O.
Thanks for answering. Please include steps and explanation as possible.