Optimum Angle for Jumping: Height & Distance

[icecomet]

Homework Statement

What is the optimum angle for greatest height? What is the greatest optimum for greatest distance? When on a surface below the landing surfaces is the optimum angle less than or greater than 45 degrees? What is the formula for finding the distance/height of the angle?

example question:
if the BMX bike wants to jump on the ledge that is 3.5ft and 7ft away what is the amount of power he needs to use? What is the optimum angle of the jump?
2. Relevant equ


_{3. The Attempt at a Solution [/b]
I think the optimum angle for a landing surface above the starting surface is greater than 45 degrees. I have no idea what the formula is though.}

 

[rl.bhat]

In projectile motion, the greatest height is achieved when the object is projected directly upwards. For other things just find the equation of a projectile motion.

 

[nlightner]

Your response:
I would first clarify that the optimum angle for jumping would depend on various factors such as the initial velocity, the mass of the object, and air resistance. However, assuming these factors are constant, the optimum angle for greatest height would be 90 degrees (straight up) and the optimum angle for greatest distance would be 45 degrees. This is because at 90 degrees, all the initial velocity is directed upwards, maximizing the height reached. At 45 degrees, the initial velocity is split equally between horizontal and vertical components, resulting in the maximum distance travelled.

When jumping from a surface below the landing surface, the optimum angle would be less than 45 degrees. This is because the initial velocity would need to be directed more vertically in order to overcome the difference in height between the two surfaces.

The formula for finding the distance/height of the angle would depend on the specific situation and would involve equations of motion and trigonometry. For the example question, we would need to know the initial velocity of the BMX bike and the angle at which it takes off in order to calculate the amount of power needed and the optimum angle of the jump.