Answer:
displacement is 41√2 m and 45º; velocity is 15 √2 m/s and 315º and the acceleration is 0.786 m/s² and 315º
Step-by-step explanation:
a and b) The cyclist is at a distance east and then north, we can find the displacement using the Pythagorean theorem
Xt² = X1² + X2²
Xt = √(41² + 41²)
Xt = 41 √2 m
The angle can be found by trigonometry
tan θ = X1 / X2
tan θ = 41/41 = 1
θ = 45º
c and d) the velocities are also vector magnitudes, so they can be brought in the same way as the displacements
V² = V1² + V2²
V = √ V1² + V2²
V = √[(-15)² + 15²
V = 15 √2 m/s
Tan θ = -15/15 = -1
θ = -45º
This is (270+ 45) measured from the east counterclockwise
θ = 315º
E and f) the average accelerations
Let's calculate the value of acceleration, which is also a vector
a = (Vf -Vo )/ t
The initial speed is directed south is negative and the final speed is directed east is positive
Vf = 15 m/s i^ θ = 0º
Vo = -15 m/s j^ θ = 270º
a = (15 i^ - (- 15) j^) / 27
cañculate the module
a² = (Vf² + Vo²) / t²
a = √ (15² + 15²) / 27
a = 15 √2 /27
a = 0.786 m/s²
The direction of acceleration is
tan θ = ay / ax
tan θ = -0.55 / 0.55 = -1
θ = -45º
This is (270+ 45) measured from the east counterclockwise