Question

(a) B, aiud B ,where B,+B aud B is i S parallel to C aud perpendicular ts B2 b) the ougle between B aud, the vec tor r P to Q 5 An aircraft, A, has a spoçă of 1000 km h-1. Taking the x-axis in an easterly direction and the z-axis vertically upwards, find the velocity vector A of the aircraft as it climbs steadily in a north-easterly direction and increases its height by 4km h1. A second aircraft, B, leaves at the same time and from the same point as A with a velocity vector v, 500i+8K km h. What is the relative velocity of the second aircrąft with respect to the first? Determine the distance apart of the two aircraft two hours 'after take-off.

Answer 1

Solution:

The speed east = 1000 k m /h The speed at north - east = 1000 Cos (45) Km/h = 1000/squareroot 2 K m /h The speed at Z axis = 4 K m/ h The velocity vector V^rightarrow_A = 1000/ squareroot 2 x cap + 4 z cap Km/h = 707.1 x cap + 4 z cap km/h another aircraft has velocity v_B cap = 500 x cap + 8 x cap km/h the relative velocity V_R cap = V_B cap - V_A cap = (500 x cap + 8 z cap) - (707.1 x cap + 4 z) = -207.1 x cap + 4 z cap hence V_R cap = -207.1 x cap + 4 Z cap after 2 hour The distance s = mode V_R cap times 2 km = mode - 207.1 x cap + 4 z cap times 2 km = 207.13 times 2 km = 414.26 km