Solving for initial velocity Projectile Motion

In summary, the problem involves a rock being thrown from the top of a 20 meter building at an angle of 53 degrees above the horizontal. The horizontal range of the throw is equal to the height of the building. The equations used to solve for the speed, time in the air, and velocity of the rock before it hits the ground are Vx = Vox, Vy = Voy - gt, x = xo + Voxt, and y = yo + Voy - (1/2)gt^2. The solution involves finding the time by setting the horizontal displacement equal to 20 meters and solving for t, then substituting that value into the y equation and solving for v. The displacement y is in the negative direction along gravity
  • #1
clark1089
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Homework Statement


A rock is thrown from the top of a twenty meter high building at the angle 53 degrees above the horizontal. IF the horizontal range of the throw is equal to the height of the building, what is the speed of the rock? How long is it in the air? What's the velocity of the rock before it hits the ground?



Homework Equations


Vx = Vox
Vy = Voy - gt
x = xo + Voxt
y = yo + Voy - (1/2)gt^2


The Attempt at a Solution


I use the second one and set x = to 20 and solve for the time...

20 = 0 + Vcos(53)t
t = 20/Vcos(53)

I substitute into the y equation

20 = vsin(53) - 1/2g(20/vcos(53)^2

Here is where I think I'm making the big mistake... help! :(
 
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  • #2
The displacement y is along g. So it must be -ve
So rewrite the equation and solve for v.
 

1. How do you find the initial velocity in projectile motion?

In order to find the initial velocity in projectile motion, you need to know the horizontal and vertical displacement, as well as the time it takes for the object to travel. You can use the equation v = d/t, where v is the initial velocity, d is the displacement, and t is the time.

2. What is the formula for calculating initial velocity in projectile motion?

The formula for calculating initial velocity in projectile motion is v = d/t, where v is the initial velocity, d is the displacement, and t is the time. This formula can be used to solve for the initial velocity in both the horizontal and vertical directions.

3. Can you find the initial velocity in projectile motion without knowing the displacement?

No, you cannot find the initial velocity in projectile motion without knowing the displacement. The displacement is a crucial component in the equation v = d/t, and without it, you cannot accurately calculate the initial velocity.

4. How does air resistance affect the initial velocity in projectile motion?

Air resistance can affect the initial velocity in projectile motion by slowing down the object's vertical velocity. This means that the initial velocity in the vertical direction may be lower than expected due to the force of air resistance acting against it. However, air resistance does not affect the initial velocity in the horizontal direction.

5. What are the units for initial velocity in projectile motion?

The units for initial velocity in projectile motion are typically meters per second (m/s). However, this may vary depending on the units used for displacement and time. It is important to use consistent units throughout your calculations to ensure accurate results.

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