Question

A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the verticle is:a. 0

b. 1.4
c. 24
d. 90
e. cannot be found without knowing the mass of the ball

Answer 1

Answer:c

Step-by-step explanation:

Given

radius of curve
`r=75\ m`

constant speed
`v=18\ m/s`

The angle between the vertical and the string is given by the tan inverse ratio of centripetal acceleration and acceleration due to gravity

`a_c=(v^2)/(r)`

`a_g=g`

`\tan \theta =(a_c)/(a_g)`

`\tan \theta =(v^2)/(r\cdot g)`

`\tan \theta =(18^2)/(75* 9.8)`

`\theta =23.78^(\circ)\approx 24^(\circ)`