A bridge that was 5.0m long has been washed out by the rain several days ago. How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge, the road on the far side is 2.0m lower than the road on this side.

To calculate the minimum speed required for a car to successfully jump the stream, we can make use of the principles of projectile motion.

First, we need to determine the horizontal distance the car must travel to clear the stream. In this case, the bridge length of 5.0m doesn't affect the distance since the car will be jumping over the stream. So, the horizontal distance is simply the width of the stream, which we can assume to be 5.0m.

Next, we need to calculate the vertical distance the car needs to cover to reach the lower road on the far side. In this case, the road on the far side is 2.0m lower than the road on the near side. So, the vertical distance, in this case, is 2.0m.

Now we can calculate the minimum speed required for the car to jump the stream. The speed required can be found using the kinematic equation for projectile motion:

v^2 = u^2 + 2as,

Where:
v = final velocity (which in this case is zero, as the car will have no vertical velocity after landing)
u = initial velocity (the speed of the car)
a = acceleration (which in this case is acceleration due to gravity, -9.8 m/s^2 due to the downward direction)
s = vertical distance

Plugging in the values, we have:

0 = u^2 + 2(-9.8 m/s^2)(-2.0m)

Simplifying the equation, we get:

0 = u^2 + 39.2 m^2/s^2

To solve for u, we need to isolate it:

u^2 = -39.2 m^2/s^2

Taking the square root of both sides:

u = ±√(-39.2) m/s

Since we're dealing with physical quantities, we discard the negative solution. Therefore:

u ≈ √39.2 m/s ≈ 6.26 m/s

So, the car must be traveling at a minimum speed of approximately 6.26 m/s (or 22.5 km/h) to successfully jump the stream.

Please note that this calculation assumes idealized conditions and neglects factors such as air resistance, the angle of the car's trajectory, and any potential obstacles on the far side.

nvm i got it