Refer to the diagrams shown below.
Define
a₁ = 2.5 m/s², acceleration of the car (north)
a₂ = the acceleration of the bolt relative to the car
g = 9.8 m/s²
Relative to the car, the acceleration of the bolt is
a₂² = 9.8² + 2.5² = 102.29
a₂ = 10.1 m/s²
The direction of a₂ is
θ = tan⁻¹ (2.5/9.8) = 14.3° south of the vertical.
Relative to the earth, the acceleration of the bolt is
a₂ = 10.1 m/s²
θ = 14.3°, north of the vertical.
Answer:
(a) 10.1 m/s² at a vertical angle of 14.3° southward.
(b) 10.1 m/s² at a vertical angle of 14.3° northward
