Question

A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s^2. (a.) What is the acceleration of the bolt relative to the train car? (b.) What is the acceleration of the bolt relative to the earth?

Answer 1

The bolt's acceleration relative to the train car is 0 m/s², and relative to the Earth, it has a horizontal component of 2.50 m/s² and a vertical component of 9.81 m/s².

Step-by-step explanation:

The student is asking a physics question related to relative acceleration. (a) The acceleration of the bolt relative to the train car is 0 m/s² since it was initially at rest with respect to the train car before dropping. (b) The acceleration of the bolt relative to the Earth combines the acceleration due to gravity and the acceleration of the train. This results in a compound acceleration where the horizontal component is 2.50 m/s² (train's acceleration) and the vertical component is 9.81 m/s² (gravity's acceleration).

Answer 2

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