Zero angle launch problem: Find height given inital speed and angle

In summary, the zero angle launch problem is a physics problem that involves finding the height of an object launched at an initial speed and angle of zero degrees. The initial speed and angle determine the initial velocity of the object, which is necessary to calculate the height using the equations of motion. The equations of motion used are: Vertical displacement (y) = initial velocity (v) * time (t) + 0.5 * acceleration due to gravity (g) * time^2, Horizontal displacement (x) = initial velocity (v) * time (t), Total time (t) = 2 * initial velocity (v) * sin(angle) / acceleration due to gravity (g), and Final height (h) = initial velocity
  • #1
egadda2
7
0

Homework Statement



A basketball is thrown horizontally with an initial speed of 4.40 m/s. A straight line is drawn from the release point to the landing point making an angle of 30.0o with the horizontal. WHAT WAS THE RELEASE POINT?

Homework Equations



tan[tex]\theta[/tex] = y/x
vfx= vix= 4.40 m/s
v2fy = v2iy - 2a[tex]\Delta[/tex]y

a = -g = -9.81
[c]3. The Attempt at a Solution [/b]
 
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  • #2
Hi egadda2! :smile:

(have a theta: θ :wink:)

Find the equation for x and t, and the equation for y and t, then put y = xtanθ, and eliminate t. :wink:
 
  • #3


To solve for the release point, we can use the equation vfx = vix = 4.40 m/s and the fact that the vertical component of the initial velocity is zero, since the ball is thrown horizontally. This means that v2fy = v2iy - 2a\Deltay = 0 - 2(-9.81)\Deltay = 19.62\Deltay. We can then use the formula tan\theta = y/x to find the ratio of the vertical and horizontal distances between the release point and the landing point, which is equal to 1/tan30. Solving for y, we get y = x/tan30 = 1.73x. Substituting this into our previous equation, we get 19.62\Deltay = 1.73x, which can be rearranged to solve for x, the horizontal distance. Once we know the horizontal distance, we can use the equation x = vxt to solve for the time it takes for the ball to travel from the release point to the landing point. Finally, we can use the equation y = vyt - 0.5gt^2 to solve for the height at the release point, since the vertical component of the initial velocity is zero. This will give us the height of the release point given the initial speed and angle of the ball's launch.
 

1. What is the zero angle launch problem?

The zero angle launch problem is a physics problem that involves finding the height of an object launched at an initial speed and angle of zero degrees.

2. How is the initial speed and angle related to the height in this problem?

The initial speed and angle determine the initial velocity of the object, which is necessary to calculate the height using the equations of motion.

3. What are the equations of motion used to solve this problem?

The equations of motion used are:
- Vertical displacement (y) = initial velocity (v) * time (t) + 0.5 * acceleration due to gravity (g) * time^2
- Horizontal displacement (x) = initial velocity (v) * time (t)
- Total time (t) = 2 * initial velocity (v) * sin(angle) / acceleration due to gravity (g)
- Final height (h) = initial velocity (v) * cos(angle) * total time (t) - 0.5 * acceleration due to gravity (g) * total time^2

4. What is the acceleration due to gravity used in this problem?

The acceleration due to gravity is a constant value of 9.8 m/s^2, which is the acceleration experienced by an object due to the Earth's gravitational pull.

5. How can this problem be applied in real-life situations?

This problem can be applied in situations such as calculating the height of a projectile launched at a zero angle, such as a ball rolling off a table or a bullet fired from a gun. It can also be used in sports, such as calculating the height of a basketball shot or a golf ball hit with no angle.

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