Motion & Relative Dynamics Question

In summary, to solve this problem, one would use constant acceleration kinematic equations and make assumptions such as no air resistance. The time it takes for the projectile to reach the ground can be found using the initial conditions and appropriate equations. To find the velocity on impact, one would use the horizontal and vertical components of the velocity and apply trigonometry to find the combined magnitude and angle from the horizontal. Additionally, higher mathematics may be useful in solving this problem efficiently.
  • #1
BIGEYE
20
0
My son is just starting his advanced highers physics and asks on how best to approach/solve this problem:

A projectile is launched from the top of a building with an initial speed of 20 m s-1 at an angle of 30° to the horizontal. The height of the building is 30 m.
(a) Calculate how long it takes the projectile to reach the ground.
(b) Calculate the velocity of the projectile on impact with the ground, (magnitude and direction).

Appreciate any help.

TIA
 
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  • #2
This is found by simple constant acceleration kinematic equations (equations of motion). You also allply assumptions, such as no losses due to air resistance etc.

You use the inital conditions to find the time taken to hit the ground from one of the suitable equations.

From this you can find all the other information.

For part b you find the horizontal and vertical components of the velocities (from the equations above). You then use these vectors to build a triagle, and use trigonometry to work out the combined magnitude and angle from horizontal.
 
  • #3
Thanks, that's got him thinking. To find the time it takes to hit the ground, he will first need to find the height the projectile gets to.
 
  • #4
I do not know what you meant by higher physics. However, for your son's best, you need to ask him to try higher mathmatics. It's nearly an one-step question if your son knows how to use higher mathmatics. Trust me, that's the best for your son.

[tex]\vec{g} = -9.81j, \vec{h}_{0} = 30j, v_{0} = 20, \theta_{0} = 30^o, \vec{v}_{0} = v_{0}cos\theta_{0}i + v_{0}sin\theta_{0}j[/tex]

[tex]\vec{v} = \int\vec{g}dt = \vec{v}_{0} + \vec{g}t[/tex]

[tex]\vec{r} = \int\vec{v}dt = \vec{h}_{0} + \vec{v}_{0}t + \frac{1}{2}\vec{g}t^2[/tex]
 

1. What is motion?

Motion is the change in position of an object over time. It can be described in terms of displacement, velocity, and acceleration.

2. What is relative dynamics?

Relative dynamics is the study of the motion and interactions of objects in relation to one another. It takes into account the relative positions, velocities, and accelerations of multiple objects.

3. How is relative dynamics different from classical mechanics?

While classical mechanics focuses on the motion of a single object, relative dynamics considers the interactions and motions of multiple objects in a system.

4. What are some real-life applications of relative dynamics?

Relative dynamics is used in various fields such as aerospace engineering, robotics, and celestial mechanics. It is also important in understanding the motion of particles in fluids and the behavior of molecules in chemical reactions.

5. How do we calculate relative velocities and accelerations?

Relative velocities and accelerations can be calculated using vector operations and the laws of motion. It involves considering the reference frame and the relative positions, velocities, and accelerations of the objects in the system.

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