Find Min Speed to Jump 8 Cars: 2D Homework Solution

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In summary, the problem involves a stunt driver trying to jump over 8 cars parked side by side with a horizontal ramp. Part (a) asks for the minimum speed needed for the car to clear the 1.5m high ramp and 20m horizontal distance. Part (b) asks for the new minimum speed if the ramp is tilted upward at a 10 degree angle. The equation used to solve for the initial velocity involves two equations, with two variables (t and v0). After solving for v0, the correct answer is found to be 2.05 m/s, with the error coming from a mistake in the placement of g in the equation.
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Homework Statement


A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp (Fig. 3-46). (a) With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the cars and the horizontal distance he must clear is 20m. (b) What is the new minimum speed if the ramp is now titled upward, so that "takeoff angle" is 10 degrees above the horizontal, and nothing else is changed?

http://img181.imageshack.us/img181/6396/chp3pro46sk5.th.png [Broken]

I need help on part b.
y0 = 1.5m
x = 20m.
Z = 10 degrees

Homework Equations


x = (v0 cos Z) t
0 = y0 + (v0 sin Z)t - 0.5*g*t2

The Attempt at a Solution


I have two equations in two variables, t and v0. So I solved for v0:
[tex]v_0^2 = (\frac{x^2}{2g\cos^2 Z})(\frac{1}{y_0 + x \tan Z})[/tex]

So, plugging in, I got 2.05 m/s for v0. But that has to be wrong, especially since my answer in (a) is 36m/s.

What am I doing wrong?
 
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  • #2
I know what I did wrong. I put g in the denominator, but it should be in the numerator...
 
  • #3
algebra mistake... the g should be placed on the numerater...
 
  • #4
How did you develop the equation to solve for the initial velocity?
 

1. What is the objective of "Find Min Speed to Jump 8 Cars: 2D Homework Solution"?

The objective of this homework solution is to find the minimum speed required for a car to successfully jump over 8 cars in a 2D simulation.

2. How is the minimum speed calculated for this solution?

The minimum speed is calculated by using the laws of physics, specifically the equations for projectile motion, to determine the velocity needed for the car to clear all 8 cars in the simulation.

3. What factors are taken into consideration when determining the minimum speed?

The factors taken into consideration include the distance between the cars, the height of the cars, the weight and speed of the car, and the force of gravity.

4. Is there a specific formula or algorithm used to solve this problem?

Yes, there is a specific formula known as the range equation that is used to solve this problem. It takes into account the initial velocity, angle of launch, and acceleration due to gravity to determine the minimum speed.

5. Can this solution be applied to real-life scenarios?

Yes, while this homework solution is a 2D simulation, the principles and equations used can be applied to real-life scenarios, such as calculating the speed needed for a car to clear a certain distance or height. However, there may be additional factors and variables to consider in real-life situations.

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