Particle Launched over 13.7m Gorge - Speed & Angle Calculation

  • Thread starter 7yler
  • Start date
  • Tags
    Particle
In summary, the conversation discusses the launch of a particle over a gorge with specific dimensions and at a specific angle. The launch speed is calculated to be 16 m/s, but it is incorrect due to the effect of gravity. It is also mentioned that on different planets, the required launch speed would vary.
  • #1
7yler
31
0
A particle is launched over a gorge that is 13.7 m straight across and 100 m deep. The particle is launched at an angle of 14° above the horizontal, and lands with 1.7 m to spare.
What was the particle's launch speed?
If the particle was launched at a different angle, but fell 0.5m short, what would it's launch angle be?

For the first part, I figured that the launch speed should be x, where x*cos(14 deg) = 15.4 m, so x = 16 m/s, but this is not correct. Why?
 
Physics news on Phys.org
  • #2
I got a different answer. Your answer is wrong because gravity affects the answer and you have no g in yours. On the moon a smaller speed would suffice, while on Jupiter a very large velocity is needed.

Show your work and someone will be very happy to sort it out!
 
  • #3
I realized what I was doing wrong. Thanks for the tip.
 

What is the speed of the particle launched over the 13.7m gorge?

The speed of the particle launched over the 13.7m gorge can be calculated using the formula v = √(2gh), where v is the speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the gorge (13.7m). Plugging in these values, we get v = √(2 x 9.8 x 13.7) = 15.2 m/s. Therefore, the speed of the particle launched over the 13.7m gorge is approximately 15.2 m/s.

What is the angle at which the particle was launched?

The angle at which the particle was launched can be calculated using the formula θ = tan⁻¹(√(2gh)/v), where θ is the angle, g is the acceleration due to gravity (9.8 m/s²), h is the height of the gorge (13.7m), and v is the speed of the particle. Plugging in the values, we get θ = tan⁻¹(√(2 x 9.8 x 13.7)/15.2) = 26.2°. Therefore, the particle was launched at an angle of approximately 26.2°.

What is the maximum height reached by the particle?

The maximum height reached by the particle can be calculated using the formula h = (v²sin²θ)/(2g), where h is the maximum height, v is the speed of the particle, θ is the angle at which it was launched, and g is the acceleration due to gravity (9.8 m/s²). Plugging in the values, we get h = (15.2²sin²26.2°)/(2 x 9.8) = 10.6m. Therefore, the maximum height reached by the particle is approximately 10.6m.

What is the time taken by the particle to reach the other side of the gorge?

The time taken by the particle to reach the other side of the gorge can be calculated using the formula t = (2v sinθ)/g, where t is the time, v is the speed of the particle, θ is the angle at which it was launched, and g is the acceleration due to gravity (9.8 m/s²). Plugging in the values, we get t = (2 x 15.2 x sin26.2°)/9.8 = 1.47s. Therefore, the time taken by the particle to reach the other side of the gorge is approximately 1.47 seconds.

What factors can affect the speed and angle calculation of the particle launched over the 13.7m gorge?

The speed and angle calculation of the particle launched over the 13.7m gorge can be affected by factors such as air resistance, wind speed and direction, and the shape and mass of the particle. These factors can cause deviations from the calculated values as they can impact the trajectory and velocity of the particle. In addition, human error in measurement and calculation can also affect the accuracy of the results.

Similar threads

Mechanics: calculating launch angle of projectile
    • Introductory Physics Homework Help
2
Replies
36
Views
2K
Calculate the displacement? (Projectile motion problem)
    • Introductory Physics Homework Help
Replies
3
Views
1K
Projectile Motion: Determining Launch Angle
    • Introductory Physics Homework Help
Replies
5
Views
1K
Egg tossing crime -- From what location was the egg thrown?
    • Introductory Physics Homework Help
Replies
14
Views
2K
Projectile Launching Question(multiple parts)
    • Introductory Physics Homework Help
Replies
3
Views
888
Rocket momentum through a cloud of particles
    • Introductory Physics Homework Help
Replies
1
Views
2K
Speed of the particle at a height h
    • Introductory Physics Homework Help
Replies
9
Views
1K
Projectile motion - velocity and distance
    • Introductory Physics Homework Help
Replies
2
Views
4K
Solve Ball Swinging Problem with Different Formulas and Calculations
    • Introductory Physics Homework Help
Replies
2
Views
2K
Calculate initial speed of an athlete - projectile motion
    • Introductory Physics Homework Help
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top