Solve Stone Thrown from 40m Tower at 60° Angle: Find Speed

  • Thread starter badman
  • Start date
In summary, The stone was thrown from the top of a 40m tower at an angle of 60 degrees above the horizontal and hit the ground at a point 100m from the base of the tower. To find the speed at which the stone was thrown, you will need to calculate the time it takes for the stone to travel 100m horizontally, as there is no acceleration in the horizontal direction. You can use the equations for horizontal and vertical displacement to solve for time. The final answer for the speed of the stone just before it hits the ground is 29.x m/s, with a time of 6.x seconds.
  • #1
badman
57
0
A stone trown from the top of a 40m tower at an angle of 60 degrees above the horizontal hits the ground at the point 100m from the base of the tower.

find the speed at which the stone was thrown?

fine the speed of the stone just before it hits the ground? I am sure i can get the answer to this with the help of the first.

it doesn't give you the time. :confused:
 
Physics news on Phys.org
  • #2
You'll need to calculate the time. For the first bit though, you don't need the time. Remember, you can consider horizontal and vertical motion separately. What can you say about the horizontal motion (assuming you're neglecting air resistance and stuff)?
 
  • #3
well you know that the the time it takes for the stone to travel the 100m in the horizontal direction is the same amount of time that it travels in the vertical direction.
So ask yourself how long does it take the stone to travel 100m horizontally.
 
  • #4
remember that there is no acceleration in the horizontal direction.
 
  • #5
Grr, that's what I meant.
 
  • #6
this is the displacement in the horizontal directon

[tex]x-x_0=v_0(\cos{\theta})t[/tex]

this is the displacemt in the vertical direction

[tex]y-y_0=v_0(\sin{\theta})t-\frac{1}{2}gt^2[/tex]

solve for time in the first equation and plug it into the second equation. :biggrin:
 
  • #7
but what would V_0 equal too?
 
  • #8
any one know ??
 
  • #9
neone can give me some hints here.
 
  • #10
You should develop the system of equations

[tex] 100 = v_0 \cos\left(\frac{\pi}{3}}\right) t [/tex]

[tex] -40 = v_0 \sin\left(\frac{\pi}{3}}\right) t - \frac{1}{2}gt^2[/tex]

Two equations, two unknowns.
 
  • #11
hey thanks a lot for ur time man, i already solved it. a lot of work to twist the equations around.
 
  • #12
show us your solution.
 
  • #13
I got 29.x m/s and 6.x sec
 

1. What is the equation used to solve for the speed of a stone thrown from a 40m tower at a 60° angle?

The equation used to solve for the speed of a stone is 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 tower (40m).

2. How do I determine the initial velocity of the stone?

To determine the initial velocity of the stone, you will need to use the equation v₀ = vcosθ, where v₀ is the initial velocity, v is the speed calculated in the first equation, and θ is the angle at which the stone is thrown (60°).

3. What units should be used for the height and speed in the equations?

The height should be in meters (m) and the speed should be in meters per second (m/s).

4. Can this equation also be used to solve for the distance traveled by the stone?

Yes, this equation can also be used to solve for the distance traveled by the stone. To do so, you will need to use the equation d = v₀t + ½at², where d is the distance, v₀ is the initial velocity calculated in the second equation, t is the time the stone is in flight, and a is the acceleration due to gravity (9.8 m/s²).

5. Can this equation be used for objects other than a stone thrown from a tower?

Yes, this equation can be used for any object that is thrown or launched with an initial velocity and angle. It is commonly used in projectile motion problems in physics.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
905
  • Introductory Physics Homework Help
Replies
4
Views
1K
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
957
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
Back
Top