Maximize Stone's Height Thrown From 56m Building - 2d Kinematics Help

In summary, the problem given involves a stone being thrown at an angle of 36.9 degrees above the horizontal at a speed of 24.0 m/s from a building 56m high. The question asks for the maximum height that the stone reaches with respect to the ground. To solve this problem, one can use basic kinematic equations and divide the motion into horizontal and vertical components. By finding the vertical component of the velocity and using the relationship between velocity, acceleration due to gravity, and time, one can determine the maximum height reached by the stone.
  • #1
Shyotic
1
0

Homework Statement



A stone is thrown at an angle of 36.9 above the horizontal at 24.0 m/s from a building 56m high. What is the maximum height (with respect to the ground) that the stone reaches?

Homework Equations



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The Attempt at a Solution


No clue. Have a picture drawn and all my knowns and unknowns but not sure what the solution is, or how you arrive at it.
 
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  • #2
Check your textbook, class notes, or the web for suitable Relevant Equations. You should have a set of basic kinematic equations in your inventory of handy formulas (sometimes called the SUVAT equations of motion). It's not possible to have "No clue" if you're enrolled in a class teaching the subject :smile:

So what equation(s) are relevant?
 
  • #3
Welcome to PF;
There is a good chance that you have just been covering the kind of mechanics that this relates to called "ballistics". Does that ring a bell?
You should go through your course notes for equations and examples to do with this.

In all ballistics problems, a good place to start is:
Divide the motion into horizontal and vertical components - and draw a separate v-t graph for each one: one above the other. Make sure the time-axes have the same scale.
 
  • #4
Here is my strategy to solve this question, forgive me if it is wrong:

1) Draw a diagram of the situation (its good that you did it)
2) Find the vertical component of the velocity vy using basic trigonometry
3) Then find the vertical height (clues: consider the relationship between vy,
g and t)

Hopefully this may help you further!
 
  • #5


I can provide a response to this problem using the principles of 2D kinematics. First, let's identify the knowns and unknowns in this problem:

Knowns:
- Initial velocity (vi) = 24.0 m/s
- Launch angle (θ) = 36.9° above the horizontal
- Building height (h) = 56m
- Acceleration due to gravity (g) = 9.8 m/s^2

Unknown:
- Maximum height (hmax)

To solve for the maximum height, we can use the following equation:

hmax = h + vi^2sin^2(θ)/2g

Substituting the known values into this equation, we get:

hmax = 56m + (24.0 m/s)^2sin^2(36.9°)/(2*9.8 m/s^2)

Solving for hmax, we get a maximum height of approximately 61.5 meters. This means that the stone reaches a maximum height of 61.5 meters above the ground before falling back down.

I hope this helps with your homework and understanding of 2D kinematics. Remember to always clearly identify your knowns and unknowns and use the appropriate equations to solve problems like this.
 

1. How do you calculate the maximum height that a stone can be thrown from a 56m building using 2D kinematics?

The maximum height of a stone thrown from a 56m building using 2D kinematics can be calculated using the formula h = (v02sin2θ)/2g, where h is the maximum height, v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

2. How does the angle of projection affect the maximum height of the stone?

The angle of projection directly affects the maximum height of the stone. The higher the angle, the higher the maximum height will be. This is because a higher angle results in a higher vertical component of the initial velocity, which contributes to a higher maximum height.

3. Can you use 2D kinematics to calculate the maximum height of an object thrown from a building at an angle?

Yes, 2D kinematics can be used to calculate the maximum height of an object thrown from a building at an angle. This is because 2D kinematics deals with the motion of objects in two dimensions, taking into account both the horizontal and vertical components of the motion.

4. Is it necessary to know the initial velocity of the stone to calculate the maximum height?

Yes, the initial velocity is a crucial component in calculating the maximum height of the stone using 2D kinematics. Without knowing the initial velocity, the calculation cannot be accurately performed.

5. How does the acceleration due to gravity affect the maximum height of the stone?

The acceleration due to gravity plays a significant role in determining the maximum height of the stone. As gravity constantly acts on the stone, it causes the vertical component of the initial velocity to decrease, resulting in a decrease in the maximum height. The acceleration due to gravity is typically considered to be 9.8 m/s2 in most 2D kinematics problems.

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