Car A negotiates a curve of 60 m radius at a constant speed of 50 km/h. When A passes the position shown, car B is 30 m from the intersection and is accelerating south toward the intersection at the rate of 1.5 m/s2. Determine the acceleration which A appears to have when observed by an occupant of B at this instant

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To determine the acceleration that car A appears to have when observed by an occupant of car B at this instant, we need to consider the relative motion of car A with respect to car B.

Let's break down the problem step-by-step:

Step 1: Convert the speed of car A from km/h to m/s.
Given: Speed of car A = 50 km/h

The conversion factor to convert km/h to m/s is 1 km/h = 0.2778 m/s.
So, the speed of car A in m/s = 50 km/h * 0.2778 m/s = 13.89 m/s.

Step 2: Determine the velocity of car A relative to car B.
Given: Car A is passing the position shown, and car B is accelerating towards the intersection.

At this instant, car B has a velocity relative to our reference frame that is increasing due to its acceleration towards the intersection. Therefore, the velocity of car B is continuously changing.

The velocity of car A relative to car B is the difference between their velocities.

Step 3: Calculate the distance between car A and car B when car A passes the position shown.
Given: The radius of the curve that car A is negotiating = 60 m
The distance between car A and the intersection when car A passes the position shown = 30 m

The distance between car A and car B is equal to the distance between the intersection and car B, plus the distance between car A and the intersection when car A passes the position shown.

Therefore, the distance between car A and car B = 60 m + 30 m = 90 m.

Step 4: Use the distance and the time it takes for car A to cover that distance to calculate the velocity of car A relative to car B.
The time it takes for car A to cover the given distance can be calculated using the formula:
Distance = Velocity * Time

Rearranging the formula, we get:
Time = Distance / Velocity

The time it takes for car A to cover the distance of 90 m is given by:
Time = 90 m / 13.89 m/s ≈ 6.48 s

Step 5: Determine the acceleration of car A as observed by an occupant of car B.
To calculate the acceleration of car A as observed by an occupant of car B, we need to consider the change in velocity of car A relative to car B over the given time interval.

Acceleration = Change in velocity / Time

Since car A is moving in a circular path with constant speed, its velocity does not change in magnitude. However, there is a change in direction, resulting in an acceleration towards the center of the curve. This is known as the centripetal acceleration, given by the formula:

Centripetal Acceleration = (Velocity^2) / Radius

Plugging in the values, we get:
Centripetal Acceleration = (13.89 m/s)^2 / 60 m = 3.209 m/s^2

Therefore, the acceleration of car A as observed by an occupant of car B is approximately 3.209 m/s^2.

To determine the acceleration that Car A appears to have when observed by an occupant of Car B at the given instant, we need to calculate the relative acceleration between the two vehicles.

Here's how to find the relative acceleration:

1. First, we convert the speed of Car A from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, Car A's constant speed of 50 km/h can be converted to (50 x 0.2778) = 13.89 m/s.

2. Next, we need to find the acceleration of Car A as it negotiates the curve. To do this, we use the formula for centripetal acceleration, which is expressed as a = v^2 / r, where v is the velocity and r is the radius of the curve.

Given that the radius of the curve is 60 m and the speed of Car A is 13.89 m/s, we can calculate the centripetal acceleration of Car A as follows:

a = (13.89^2) / 60
= 3.23 m/s^2 (rounded to two decimal places)

3. Now, let's determine the relative acceleration between the two cars. Since Car B is accelerating toward the intersection at a rate of 1.5 m/s^2, we need to subtract this acceleration from the centripetal acceleration of Car A:

Relative acceleration = Centripetal acceleration of Car A - Acceleration of Car B

Relative acceleration = 3.23 m/s^2 - 1.5 m/s^2
= 1.73 m/s^2 (rounded to two decimal places)

Therefore, the acceleration that Car A appears to have when observed by an occupant of Car B at this instant is 1.73 m/s^2.