A 10000 car comes to a bridge during a storm and finds the bridge washed out. The 700 driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 20.0 above the river, while the opposite side is a mere 1.60 above the river. The river itself is a raging torrent 60.0 wide.
Feet, meters? Kg or pounds? g is 9.8 m/s^2 or 32 ft/s^2 ????
The mass does not matter here.
Use
drop = (1/2) g t^2 in whatever units
to solve for t
t = sqrt (2 drop/g)
that is time in air
distance = initial speed u * t
so
60 whatever units = u * sqrt (2 drop/g)
u needed = 60 sqrt(g/{2 drop})
-- For this question, I know how to find the initial speed. If it asks, "What is the speed of the car just before it lands safely on the other side?" how do i calculate that because it's not the same as final velocity right?
---------------------------------
you got u, the horizontal speed
v = g t
which is the vertical speed at landing
s = sqrt (u^2 + v^2)
Units are Newtons and Meters
Questions are, How fast must the car be traveling to land safely on the other side? and What is the speed of the car just before it lands?
To determine whether the car can successfully leap across the river, we need to calculate the horizontal distance it needs to cover. We can use the concept of projectile motion to solve this problem.
First, let's break down the given information:
- Initial height (h1) of the car = 20.0 m
- Final height (h2) of the opposite side = 1.60 m
- Width (d) of the river = 60.0 m
We need to find the horizontal distance that the car needs to travel to reach the opposite side of the river. To do this, we can use the equation:
d = v0x * t
where:
- d is the horizontal distance
- v0x is the horizontal component of the car's velocity
- t is the time it takes for the car to reach the opposite side
To find v0x, we'll use the conservation of energy principle. The initial potential energy of the car is m * g * h1, where m is the mass of the car (10,000 kg) and g is the acceleration due to gravity (9.8 m/s^2). The final potential energy of the car is m * g * h2.
Using the conservation of energy equation:
m * g * h1 = m * g * h2 + (1/2) * m * v0x^2
Simplifying the equation, we get:
h1 - h2 = (1/2) * v0x^2 / g
Substituting the known values:
20 - 1.60 = (1/2) * v0x^2 / 9.8
18.4 = (1/2) * v0x^2 / 9.8
Multiplying both sides by 9.8:
179.92 = (1/2) * v0x^2
359.84 = v0x^2
Taking the square root of both sides:
v0x ≈ 18.97 m/s
Now that we have the horizontal component of the car's velocity, we can calculate the time it takes for the car to reach the other side of the river.
Using the equation:
d = v0x * t
Substituting the given values:
60 = 18.97 * t
Simplifying the equation:
t ≈ 3.16 s
Therefore, the car would take approximately 3.16 seconds to reach the other side of the river if it successfully leaps across.