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
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
Answers
Damon
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
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