A daredevil is dead set on jumping the Grand Canyon at its narrowest point (180 meters across). He has set up a ramp at 25 degrees and the ramp's release point is 20 meters above the rim of the canyon. He claims that his bike will be going 40m/s by the time he leaves the ramp. A corporate sponsor of the jump offers you a million dollars if you place a target on the other side and he hits your target. Where do you place your target? Other than increasing his speed, what advice would you offer the daredevil to increase his odds of landing the jump safely?
156.96 meters he don't make it. Increase angle
To determine where to place the target for the daredevil, we need to calculate the range of his jump. The range is the horizontal distance covered by an object in projectile motion.
To calculate the range, we need to use the following formula:
Range = (velocity^2 * sin(2θ)) / g
Where:
- velocity is the initial velocity of the bike (40 m/s)
- θ is the angle of the ramp (25 degrees)
- g is the acceleration due to gravity (9.8 m/s^2)
Plugging in the values, we get:
Range = (40^2 * sin(2 * 25)) / 9.8
Using this formula, we can calculate the range to be approximately 256.2 meters.
Therefore, to increase the daredevil's odds of landing the jump safely, you should place the target at a distance of around 256.2 meters from the ramp.
In addition to increasing his speed, here are some other pieces of advice you could offer the daredevil to increase his chances of landing the jump safely:
1. Optimize the launch angle: Experiment with different launch angles to find the optimal angle that maximizes distance while minimizing the risk of overshooting or falling short. This could be done through trial and error or by using simulation software.
2. Improve aerodynamics: Streamlining the daredevil's bike and outfit can reduce air resistance, allowing for smoother and more predictable flight. This could involve reducing protruding parts, adjusting body posture, and wearing aerodynamic clothing.
3. Enhance bike stability: Ensure the bike is properly balanced and has sufficient grip. Adding stabilizing features such as fins or adjusting tire pressure can help maintain control during the jump.
4. Precision timing: Coordinate the launch with wind conditions to take advantage of tailwinds that may enhance the jump distance. Avoid launching during adverse weather conditions that might negatively affect the jump.
5. Safety measures: Install safety features like a parachute or an emergency landing system that can be activated if necessary. Conduct thorough safety inspections of the ramp and make sure it can handle the forces exerted during the jump.
Remember, attempting such a dangerous stunt involves significant risks, so utmost caution and careful planning should be taken into consideration.