Acar moves horizontally with a constant acceleration of 3 m/s 2 . a ball is suspended by a string from the ceiling of the car. the ball does not swing, being at rest with respect to the car. what angle does the string make with the vertical?

The string make with the vertical an angle of 17.8°

Explanation:

The ball will move backwards until the horizontal component of its weight is accelerating it by 3 m/(s^2).

The horizontal component of its weight is calculated as follows

m*g*sinθ

The acceleration of the car is

m*a

a is the acceleration of the car (3 m/(s^2)), m is the mass of the ball, g is the gravitational acceleration (9. 81 m/(s^2)), and θ is the angle between the string and the vertical.

Notice that the ball doesn't swing, so the forces are at equilibrium, then:

m*g*sinθ = m*a

θ = arcsin(a/g)

θ = arcsin(3/9.81)

θ =  17.8 °