Maximizing Projectile Range: Motorcycle Daredevil Bus Jump

In summary, the conversation involves a motorcycle daredevil attempting to jump across as many buses as possible. The takeoff ramp is at an angle of 18.0 degrees and the buses are 2.74m wide. The cyclist has a speed of 33.5m/s. The question is, what is the maximum number of buses the cyclist can jump? To solve this problem, the conversation discusses using a range equation and finding the time t. Another question that is addressed is how long it takes for a ball with an initial vertical velocity of 10.35m/s to return to its starting height. The conversation concludes by discussing the use of a parabolic path and setting up a table of values to find the maximum number
  • #1
gsr_4life
3
0
A motorcycle daredevil is attempting to jump across as many buses as possible. The takeoff ramp makes an angle of 18.0 degrees above the horizontal, and the landing ramp is identical to the takeoff ramp. The buses are parked side by side, and each bus is 2.74m wide. The cyclist leaves the ramp with a speed of 33.5m/s. What is the max number of buses the cyclist can jump?
I know that this is a question of range involving a vector x. I know that Vo =33.5m/s, Vox= 31.86m/s and Voy= 10.35m/s using sin and cos of 18degrees. What I am having trouble with is finding time "t" so I can use the range equation. I am not even sure if I am going about this right. Any help would be great, thanks.
 
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  • #2
If you shoot a ball up into the air with the initial vertical velocity of Voy= 10.35m/s, how long before it comes back down to its starting height? (And what will its downward Vy be then?)
 
  • #3
Realize your projectile takes a parabolic path, therefore [tex]d = v_ot + 1/2at^2[/tex], where d = 0.
 
  • #4
Got it!

I set up a table of values for displacement of y=0, a=-9.8, Vo=10.35 and used the equation y=Vot+1/2a * (t squared) and plugged t into the equation Voxt=R and divided it by 2.74 = 24 buses
 

Related to Maximizing Projectile Range: Motorcycle Daredevil Bus Jump

What is projectile motion?

Projectile motion refers to the motion of an object that is launched or thrown and then moves through the air under the influence of gravity. Examples of projectile motion include a thrown baseball, a kicked soccer ball, or a fired cannonball.

What factors affect the range of a projectile?

The range of a projectile is affected by its initial velocity, the angle at which it is launched, and the acceleration due to gravity. Air resistance can also have an impact on the range, but it is typically ignored in basic projectile motion calculations.

How can the range of a projectile be calculated?

The range of a projectile can be calculated using the formula R = (v^2 sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This formula assumes a flat surface and no air resistance.

What is the optimal launch angle for maximum range?

The optimal launch angle for maximum range is 45 degrees. This is because at this angle, the initial velocity is divided equally between the horizontal and vertical components, allowing the projectile to stay in the air for the longest amount of time.

How does increasing the initial velocity affect the range of a projectile?

Increasing the initial velocity will increase the range of a projectile, as long as the launch angle remains the same. This is because a higher initial velocity will result in a larger horizontal component of the velocity, allowing the projectile to travel further before hitting the ground.

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