Sheet Three Plus Solutions

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MP120, Problem Sheet Three, Relative Velocity

1. A jet airplane A is flying in an Easterly direction at 400 km/hr relative to theground. A second jet B is flying in a NE direction. Jet B appears to be flying ina direction 30o E of N relative to jet A. Deduce the speed of jet B relative to theground.

2. A ship A is headed W off the Irish coast at a speed of 5 km/hr and a second ship Bis headed SE. According to ship A, ship B appears to be heading in a direction of

20o S of E. Deduce the speed of ship B relative to a fixed observer on the nearbycoastline.

3. Rain is falling vertically downwards with a speed of 20 m/s relative to the air.It is blown by a horizontal west wind of speed 30 m/s. A car is travelling Norththrough Galway City at 60 km/hr.

Find the velocity of the rain from the point of view of a passenger in the car.

Identify both the speed and direction of this relative velocity.

4. A man travelling SE at 2

2 km/hr notices that the wind appears to come fromthe NE. On trebling his speed while still heading in the same direction, he noticesthat the wind appears to come from the E. Find the velocity of the wind andidentify both the wind speed and the wind direction.

5. Two particles A and B with initial positions (in m) (5i

13j) and (2i

j) have

constant velocities (in m/s) (2ij) and (3i 5j) respectively. Show that twoparticles collide and find when and where this occurs.

6. Two particles A and B have velocities (in m/s) of (3i + 29j) and (3i + 21j)respectively. Find rB|A, the position ofB relative to A for all t, given that rB|A =56i+ 8j (in m) at t = 0 Hence find the time when A and B are closest together


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25k m/s towards a rabbit in a nearby field some 150 m directly East.

If the hawk commences its descent from a height of 80 m at the instant the swallowis observed leaving the top of the pole, find the time when they are closest togetherand how far apart they are at that time.


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Sheet Three Plus Solutions

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