Exploring the Impact of Density on Trajectory

In summary, the calculations and data provided allow for the calculation of the dimensions and speed needed for a stuntman to successfully cross the Grand Canyon on a motorcycle. The total horizontal distance to be covered is 52 meters, with a clearance of 6 meters on either side. The ramp is set at a slope of 45 degrees, and the stuntman will reach a speed of 22.6 m/s (49.7 mi/h) at the end of the ramp to safely cross the canyon. However, more data is needed to calculate the total height the stuntman and motorcycle will fall before reaching the ramp.
  • #1
jillz
15
0
why does lowering the density change the trajectory?

why does lowering the density change the trajectory?
Is this a basic/general question or is more information needed??
totally lost...:confused:
 
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  • #2
Not sure what you're asking here...

If you're asking about an object that is put into flight, and then has mass taken away while maintaining the same volume, then it can easily be seen that the trajectory will change by looking at its kinetic energy. If the mass goes down, the velocity has to go up, thus changing the trajectory from its original path.

Not sure exactly when something like that could happen in real life, though.
 
  • #3
jillz said:
why does lowering the density change the trajectory?
Is this a basic/general question or is more information needed??
totally lost...:confused:

Hi jillz! Welcome to PF! :smile:

If you're talkling about light, it's because a higher density slows the light down (as one would expect). For details, see:
 
  • #4
Echo that welcome, Jillz.
In simple terms, anything traveling through a medium requires a certain amount of energy to do so, as it has to push stuff out of the way in order to progress. The denser that medium is, the more energy is needed because it's harder to push. (Think of swinging your arm around under water as opposed to in air.) Something in ballistic flight (ie: unpowered after launch) will run out of momentum sooner and thus start back down closer to the launch site.
Even without gravity, the trajectory will change in that it will take longer to get to where it's headed or even stop completely before getting there, even though the actual flight path doesn't change.
 
  • #5
With all of the calculations/data below, is it still possible to calculate the dimensions for the motorcycle falling/landing from the jump? Or is more data needed? What type of calculation would be used to find the dimensions for a falling object?? Thanks for any help! Jillz:wink:


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Stunt man Joe wants to cross the Grand Canyon on his motorcycle. His crew has set up a ramp on one side of the canyon. Several factors will determine his safe landing on the other side. Assume that he decides to perform the stunt on a quiet day so that the drag from the wind will not have any effect on his motion.

Assume that Joe has to cross a distance of 40 m, leaving some clearance on both sides. The clearance on either side will be 6 m. Total horizontal distance that he needs to cover is 52 m to safely land on the other side.

The crew decides to set up the ramp at an inclination of 45o.
i.e. the slope of the ramp, θ = 45o

His motion from the time he leaves the ramp to the point where he is at the same level on the other side of the canyon. During the time he is airborne, his acceleration is the acceleration of gravity.

Using s = ut + ½ a t2
s = arc length

Horizontally: 52 = u cos θ t

t = 52 / u cos θ ------------------------------- (1)

Net vertical distance he traveled = 0

Vertically: 0 = u sin θ t - ½ g t2

u sin θ = ½ g t

Substituting from (1)

u sin θ = ½ g (52 / u cos θ)
u2 = 52g/ 2 cos θ sin θ = 52g/ 2 cos 45 sin 45 = 509.6

u (speed) = 22.6 m/s

He should reach a speed of 22.6 m/s (49.7 mi/h) at the end of the ramp in order to safely cross the Grand Canyon.
 
  • #6
thanks for the input! and cute pict!

thanks for the input! and cute pict!
Danger said:
Echo that welcome, Jillz.
In simple terms, anything traveling through a medium requires a certain amount of energy to do so, as it has to push stuff out of the way in order to progress. The denser that medium is, the more energy is needed because it's harder to push. (Think of swinging your arm around under water as opposed to in air.) Something in ballistic flight (ie: unpowered after launch) will run out of momentum sooner and thus start back down closer to the launch site.
Even without gravity, the trajectory will change in that it will take longer to get to where it's headed or even stop completely before getting there, even though the actual flight path doesn't change.
 
  • #7
jillz said:
cute pict!

Thanks; it's clipped from my wedding photo.
 
  • #8
With all of the calculations/data below, is it still possible to calculate the dimensions for the motorcycle falling/landing from the jump? Or is more data needed? What type of calculation would be used to find the dimensions for the total height the stuntrider/cycle will fall before hitting the ramp.Thanks for any help! Jillz


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Stunt man Joe wants to cross the Grand Canyon on his motorcycle. His crew has set up a ramp on one side of the canyon. Several factors will determine his safe landing on the other side. Assume that he decides to perform the stunt on a quiet day so that the drag from the wind will not have any effect on his motion.

Assume that Joe has to cross a distance of 40 m, leaving some clearance on both sides. The clearance on either side will be 6 m. Total horizontal distance that he needs to cover is 52 m to safely land on the other side.

The crew decides to set up the ramp at an inclination of 45o.
i.e. the slope of the ramp, θ = 45o

His motion from the time he leaves the ramp to the point where he is at the same level on the other side of the canyon. During the time he is airborne, his acceleration is the acceleration of gravity.

Using s = ut + ½ a t2
s = arc length

Horizontally: 52 = u cos θ t

t = 52 / u cos θ ------------------------------- (1)

Net vertical distance he traveled = 0

Vertically: 0 = u sin θ t - ½ g t2

u sin θ = ½ g t

Substituting from (1)

u sin θ = ½ g (52 / u cos θ)
u2 = 52g/ 2 cos θ sin θ = 52g/ 2 cos 45 sin 45 = 509.6

u (speed) = 22.6 m/s

He should reach a speed of 22.6 m/s (49.7 mi/h) at the end of the ramp in order to safely cross the Grand Canyon.
 
  • #9
jillz said:
Using s = ut + ½ a t2
s = arc length

The 's' above is not the arc length; it is the vertical distance traveled in time 't'. You are writing arc length, but applying the same formula for vertical displacement!

The rest seems to be all right, but I haven't checked the arithmetic.
 
  • #10
So I would use the calculation: s = ut + ½ a t2
to find the distance the rider/bike would fall from the highest point down to the ramp??
 
  • #11
If things don't appear to make sense in here, that's because two different threads have been merged into one.

jillz: please do not make multiple threads of the same thing. Confine this question to ONLY this thread.

Zz.
 

FAQ: Exploring the Impact of Density on Trajectory

1. What is density and how does it affect trajectory?

Density refers to the amount of mass per unit volume of a substance. In terms of trajectory, density affects the path an object takes due to the resistance it experiences from the medium it is moving through. Objects with higher density will experience more resistance and therefore have a shorter trajectory compared to objects with lower density.

2. How can density be measured in a scientific experiment?

Density can be measured by dividing the mass of an object by its volume. This can be done by using a balance to measure the mass and a ruler or other measuring instrument to determine the volume. Alternatively, density can also be calculated by using the formula D = m/V, where D is density, m is mass, and V is volume.

3. What are some examples of how density affects trajectory in real life?

Density has a significant impact on the trajectory of objects in various scenarios. For example, a plane's trajectory can be affected by the density of the air it is flying through, while a boat's trajectory can be influenced by the density of the water it is sailing on. In sports, the trajectory of a golf ball or a baseball can be altered by the density of the air and the materials used to make the ball.

4. How does changing the density of a medium affect the trajectory of an object?

Changing the density of a medium can have a direct impact on the trajectory of an object. For instance, increasing the density of a fluid can cause an object to sink faster, resulting in a shorter trajectory. On the other hand, decreasing the density of a fluid can lead to a longer trajectory as the object experiences less resistance.

5. What other factors besides density can affect the trajectory of an object?

Besides density, other factors that can affect an object's trajectory include the shape and size of the object, the force applied to it, and the medium it is moving through (such as air or water). Additionally, external forces like gravity and air resistance can also impact the trajectory of an object.

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