Answer:
East
Explanation:
In circular motion, the velocity of the object will always be tangential to the radius of the circle. In this case, since the car is at the northernmost point of the circular track, then it must be moving right or towards the east, no matter what the acceleration might be at that very moment or what the radius of the track is. If it's moving clockwise, then it moves right (towards the east).
The concept of total acceleration and trigonometry allows to find the result for the direction of the velocity or acceleration of the body is:
41.4 South of East
Given parameters
Radius r = 1440 m
Speed v = 36 m / s
Acceleration a = 1.2 m / s
To find
Speed direction
Kinematics studies the motion of bodies, looking for relationships between position, velocity and acceleration.
In the case of circular motion, there is an acceleration that changes the direction of the velocity, but not its modulus, this acceleration is called centripetal and is expressed by the relationship.
[tex]a_c= \frac{v^2}{R}[/tex]
If there is an acceleration in the same direction of movement, it is called tangential acceleration and is given by:
[tex]a_t = \frac{dv}{dt}[/tex]
The total acceleration of the body is given by the Pythagorean theorem, see attached.
[tex]a^2 = a_c^2+ a_t^2[/tex]
Let's look for centripetal acceleration.
[tex]a_c = \frac{36^2}{1440} \\ a_c = 0.9 m/s^2[/tex]
We look for tangential acceleration.
[tex]a_t^2 = a^2 -a_c^2 \\a_t =\sqrt{1.2^2 - 0.9^2} \\a_t = 0.94 m/s^2[/tex]
They indicate that the body is at the northernmost point of the circle, therefore the direction of the tangential acceleration is towards the east, let's use trigonometry to find the direction of the total acceleration.
tan θ = [tex]\frac{a_t}{a_c}[/tex]
θ = tan⁻¹ [tex]\frac{a_t}{a_c}[/tex]
θ = tan⁻¹ [tex]\frac{0.794}{0.9}[/tex]
θ = 41.4º
This direction is with respect to the vertical pointing towards the center of the circle, with respect to the cardinal points the direction of the acceleration is:
41.4º South of East
In conclusion using the concept of total acceleration and trigonometry we can find the direction of the change of the velocity of the body is:
41.4 South of East
Learn more here: brainly.com/question/3388038
