Two cars lost in a blinding rainstorm are traveling across a large field, each thinking they are on the road. They collide. If the distance between them is 174 meters and the red car is traveling at 6 mph at a 45 degree angle toward the impact point, and the blue car is traveling at 6.1 mph at 60 degree angle to the impact point. How much time passes.
Using the formula x=x0+v0t.
I am not understanding how to manipulate the numbers in order to come up with the answer of 53.4 seconds...please help
The white car leaves the stop sign to make a left turn, the van is coming straight at the White car before impact the van leaves 20ft of skid marks .
How fast was the van traveling?
To solve this problem, you can use the formula x = x0 + v0t, which represents the position (x) of an object as a function of its initial position (x0), initial velocity (v0), and time (t).
Let's consider the red car first. The initial position (x0) of the red car is not given, but we can assume it is at the origin (0,0) since it thinks it is on the road. The speed (v0) of the red car is given as 6 mph, but we need to convert it to meters per second to maintain consistency with the unit of distance given. Since 1 mile is approximately equal to 1609.34 meters and 1 hour is equal to 3600 seconds, the speed of the red car is 6 mph * (1609.34 meters / 1 mile) * (1 hour / 3600 seconds) ≈ 2.682 m/s.
The blue car's initial position (x0) is also not given, but we can assume it starts 174 meters away from the red car since that is the distance between them. We need to find its initial velocity (v0) by resolving its velocity into horizontal and vertical components. The speed of the blue car is given as 6.1 mph, which, similarly to the previous case, is approximately equal to 2.725 m/s.
The blue car's velocity can be resolved into horizontal and vertical components as follows:
Horizontal component: v0_hor = v0 * cos(angle) = 2.725 m/s * cos(60°)
Vertical component: v0_ver = v0 * sin(angle) = 2.725 m/s * sin(60°)
Now we are ready to find the time (t) using the formula x = x0 + v0t. Since both cars have collided, their x-position will be the same:
0 + 2.682 m/s * t = 174 m - (2.725 m/s * sin(60°) * t)
Now we can solve this equation for t:
2.682 m/s * t = 174 m - (2.725 m/s * sin(60°) * t)
2.682 t = 174 - 2.725 * sin(60°) * t
2.682 t + 2.725 * sin(60°) * t = 174
(2.682 + 2.725 * sin(60°)) * t = 174
t = 174 / (2.682 + 2.725 * sin(60°))
Using a calculator, you can evaluate this expression and find that t ≈ 53.4 seconds.
So, the time that passes before the collision is approximately 53.4 seconds.