At t = 0 a car is due 2 km north of you heading west moving 13 km/s after 1.5 s. What is the angle in radians between you and the car from where the car was at t = 0?
d1 = 2 km.
d2 = 13 * 1.5 = 19.5 kim.
Tan A = d2/d1 = 19.5/2 = 9.75
A = 84.14 degrees = 1.47 radians.
sorry, upside down
tan angle = 19.5/2
angle = 84.14 degrees
* pi/180 = 1.49 radians
Well, let's see. If the car is 2 km north of me and heading west, it sounds like we're about to have a little drive-by party! Now, we need to find the angle in radians between us.
Since the car is moving at a constant speed of 13 km/s for 1.5 seconds, it covers a distance of (13 km/s) * (1.5 s) = 19.5 km.
Now, let's create a right-angled triangle with the car's starting position, its ending position, and a line connecting us. The horizontal side of the triangle represents the 19.5 km distance traveled by the car, and the vertical side represents the 2 km distance north of me.
So, we have a right triangle with a base of 19.5 km and a height of 2 km. To find the angle between us, we can use the inverse tangent function (tan⁻¹) which gives us the angle whose tangent is the ratio of the vertical side (2 km) to the horizontal side (19.5 km).
Plugging those values into a calculator, we get:
angle = tan⁻¹(2 km / 19.5 km) ≈ 0.102 radians.
So, the angle in radians between us and the car from where the car was at t = 0 is approximately 0.102 radians.
To find the angle in radians between you and the car, we can use trigonometry.
Let's break down the problem step by step:
1. At t = 0, the car is 2 km north of you and heading west. This means the car is directly to the left of your current position.
2. After 1.5 seconds, the car has moved a distance of 13 km west. This means it has moved directly to the left of its initial position.
3. Now, we need to find the distance between the car's initial position and its current position. Since the car has moved only left, the distance between the initial and current positions is equal to the displacement (13 km).
4. We also need to find the distance between you and the car. Since the car is directly to the left of your position, this distance is 2 km.
Now we can use the trigonometric concept of tangent to find the angle in radians between you and the car:
tangent(theta) = opposite/adjacent
tangent(theta) = 2 km / 13 km
theta = arctan(2/13)
Calculating arctan(2/13), we find that theta is approximately equal to 0.1525 radians.
Therefore, the angle in radians between you and the car from its position at t = 0 is approximately 0.1525 radians.
No way a car moves 13 km/ s but anyway
at t = 0, x = 0 and y = 2 km, call angle = 0
at t = 1.5 , -x = 1.5 * 13= 19.5 y still = 2
tan angle = 2/19.5
angle = 5.956 degrees
* pi/180 = 0.1022 radians