A car is traveling on a level horizontal rode comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side of the road the car is on 21.3m above the river, while the opposite side is mere 1.8m above the river. The rive itself is a ranging torrent 61.0m wide. How fast should the car be traveling at the time it leaves the road in order just to clear the river and the land safely on the opposite side?. What is the speed of the car just before it lands on the other side?

h = 0.5g*Tf^2 = 21.3-1.8 = 19.5 m

4.9*Tf^2 = 19.5,
Tf^2 = 3.98, Tf = 1.99 s. = Fall
time.

a. d = Xo * Tf = Xo * 1.99 = 61,
Xo = 30.6 m/s = Hor. velocity at time it leaves the road.

Well, it seems like this driver is really taking "bridge jumping" to a whole new level! Let's see if we can calculate the speed needed for this daring stunt.

To clear the river and land safely on the opposite side, the car needs to cover the horizontal distance of 61.0m while being in the air. So, we need to calculate the initial velocity (speed) required for this jump.

Let's break it down step by step:

Step 1: Determine the time it takes for the car to cross the river.
To calculate time, we can use the equation: distance = speed × time.
Since the car is in the air, the only force acting on it is gravity. So, the time it takes for the car to cross the river will be the same as the time it takes for an object (dropped from a height) to fall vertically.

Using the equation: distance = (1/2) × acceleration × time², we can find the time.
Here, the distance is 21.3m (height of the road) - 1.8m (height of the landing side) = 19.5m (total height car needs to drop).

Step 2: Calculate the time it takes for the car to cross the river.
19.5m = (1/2) × 9.8m/s² × time²
Solving for time, we have time = sqrt(2 × 19.5m / 9.8m/s²).
Calculating this, we find time ≈ 2 seconds.

Step 3: Determine the speed needed to clear the river.
To find the speed, we can use the equation: speed = distance / time.
Here, the distance is 61.0m (width of the river).
So, speed = 61.0m / 2s = 30.5m/s.

Now, just before landing on the other side, the car is still moving horizontally at the same speed, 30.5m/s.

However, it's important to note that this calculation assumes the car follows a perfect parabolic trajectory without any air resistance or other factors. In reality, attempting such a jump could be extremely dangerous and is not recommended. Safety first, folks!

Remember, even clowns know when not to take things too far! Stay safe on the roads.

To calculate the speed required for the car to safely clear the river and land on the opposite side, we can use the principles of projectiles and conservation of energy.

Step 1: Determine the vertical component of the car's velocity when it leaves the road.
The car needs to clear a vertical distance of (21.3m - 1.8m) = 19.5m. We can use the equation:

Vertical distance = (Initial vertical velocity * Time) + (0.5 * Acceleration * Time²)

Since the car starts from rest vertically, the equation simplifies to:

19.5m = (0.5 * Acceleration * Time²)

Step 2: Calculate the time required for the car to reach the opposite side of the river.
The car travels a horizontal distance of 61.0m. Horizontal distance = Horizontal velocity * Time. Since the horizontal motion is constant, the time is the same as the time from step 1.

Step 3: Find the horizontal component of the car's velocity when it leaves the road.
We know that the horizontal distance is covered with uniform motion, so the velocity remains constant. Let's call this velocity Vhoriz. We can use the equation:

Horizontal distance = Horizontal velocity * Time

61.0m = Vhoriz * Time

Step 4: Calculate the speed of the car just before it lands on the other side.
To do this, we need to find the total velocity of the car just before it lands, combining both the horizontal and vertical components. We can use Pythagoras' theorem:

Total velocity = √((Vertical velocity)² + (Horizontal velocity)²)

The car's vertical velocity is found in step 1, where it cleared a vertical distance of 19.5m. The horizontal velocity is found in step 3, where the car traveled 61.0m.

Step 5: Solve for the car's speed just before it lands.
We need to substitute the values from steps 1 and 3 into the total velocity equation and solve for the speed.

Total velocity = √(Vertical velocity² + Horizontal velocity²)

Finally, we can calculate the speed of the car just before it lands using the formula:

Speed = Total velocity / Time

Please note that the question does not provide information about the acceleration, so we assume it to be 10 m/s² for simplicity.

To solve this problem, we can use the principles of projectile motion. We need to determine the initial velocity with which the car must leave the road to safely clear the river and land on the other side, as well as the speed of the car just before it lands.

Let's break down the problem into two parts:
1. Determine the initial velocity required to clear the river.
2. Calculate the speed of the car just before landing on the other side.

1. To determine the initial velocity required to clear the river:
Using the kinematic equation for vertical motion, we can calculate the initial vertical velocity (V_y) required for the car to travel a horizontal distance (d) of 61.0m and a vertical displacement (h) of 21.3m - 1.8m = 19.5m (the difference in height between the two sides of the road).

The equation for vertical displacement is given by:
h = V_{y} * t + (1/2) * g * t^2

Here, g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time taken to reach the other side.

Since the initial vertical velocity (V_y) is zero when the car leaves the road, we can rearrange the equation to solve for t:
t = sqrt((2h) / g)

Plug in the values: h = 19.5m and g = 9.8 m/s^2, and solve for t.

2. Once we have determined the time taken to reach the other side, we can calculate the horizontal velocity (V_x) required to cover the horizontal distance of 61.0m in that time.

The equation for horizontal motion is given by:
d = V_{x} * t

Rearrange the equation to solve for V_x:
V_{x} = d / t

Now, armed with the time taken to reach the other side, we can calculate the speed of the car just before landing.

3. The final horizontal velocity (V_{xf}) just before landing will be equal to the initial horizontal velocity (V_{x}) since there is no horizontal force acting on the car after leaving the road. Hence, V_{f} = V_{x}.

In summary, to solve the problem:
1. Calculate the time (t) taken to reach the other side using the equation t = sqrt((2h) / g), where h = 19.5m and g = 9.8 m/s^2.
2. Calculate the initial horizontal velocity (V_{x}) using the equation V_{x} = d / t, where d = 61.0m and t is the value obtained in step 1.
3. The speed of the car just before landing on the other side is V_{f} = V_{x}.

Follow these steps to find the answers to the problem.

b. V^2 = Vo^2 + 2g*h.

V^2 - 0 + 19.6*19.5 = 382.2,
V = 19.5 m/s.