A 10,000N car comes to a bridge during a storm and finds the bridge washed out. The 650-N driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 16.6 m above the river, while the opposite side is a mere 7.90 m above the river. The river itself is a raging torrent 51.4 m wide. How fast should the car be traveling just as it leaves the cliff in order just to clear the river and land safely on the opposite side?

This question has already been posted on here but I need to know how they found the initial velocity.

Horizontal problem:

Speed = constant = U, the initial speed
distance = U t = 51.4 m
Vertical problem:
falls (16.6 - 7.9) = 8.7 meters DOWN
initial speed down = 0
so
8.7 = (1/2) (9.8) t^2
weight has no effect on this problem, only the acceleration of gravity
8.7 = 4.9 t^2
t^2 = 1.77
t = 1.33 seconds to9 fall
same t to reach the other bank so
U = 51.4 meters / 1.33 seconds
= 38.6 meters/sec

Thank you so much.

You are welcome !

why is the initial speed down equal to 0?

To find the initial velocity of the car, we can use the principle of conservation of energy. The car will have potential energy when it is at the top of the cliff, and this potential energy will get converted to kinetic energy as the car moves through the air. At the point of takeoff, all the potential energy will be converted into kinetic energy.

First, let's calculate the potential energy of the car when it is at the top of the cliff:

Potential energy = mass x gravity x height

The mass of the car is given as 10,000 N, and we need to convert this force into mass. We can use Newton's second law of motion to do this:

Force = mass x acceleration

Rearranging the equation, we get the mass:

Mass = Force / acceleration

The acceleration due to gravity is approximately 9.8 m/s^2. So, we can find the mass:

Mass = 10,000 N / 9.8 m/s^2

Next, let's calculate the potential energy:

Potential energy = Mass x gravity x height

Now, subtract the potential energy from the initial kinetic energy equation to get the final kinetic energy equation:

Kinetic energy = (1/2) x mass x velocity^2

Since there is no friction or air resistance, we can assume that the kinetic energy at the point of takeoff will be equal to the potential energy at the top of the cliff:

Potential energy = Kinetic energy

Mass x gravity x height = (1/2) x mass x velocity^2

Now, solve for velocity:

velocity = sqrt((2 x gravity x height) / mass)

Plug in the given values for gravity, height, and mass to find the velocity at the point of takeoff.