Question

Starting simultaneously from the same spot, O, Alvin and Bernard set out across a field in the gog. Alvin travels with velocity i + 2 j m/s and Bernard with velocity 3i + j m/s, To avoid losing each other, they hold opposite ends of 90 m string.
a) At what speed alvin travels
b) Find the direction of travel of the two people and hence the angle between their path
c) Find the position vector OA and OB at t sesonds, and hence the vector AB at that time
d)Find the value of t for which the dtring become taut

Answer 1

Alvin speed = sqrt (1^2 + 2^2) = sqrt (5)

tan Alvin = 2/1 so angle Alvin = 63.4 deg

tan Bernard = 1/3 so angle = 18.4
so
angle between = 63.4 - 18.4 = 45 degrees

OA = t i + 2t j
OB = 3t i + t j

AB = 2 t i -1 t j

d = sqrt ( 4t^2 + t^2) = t sqrt (5)
90 = t sqrt 5
t = 40.3 seconds