• runningirl
In summary, Zandor is being shot out of a cannon at a velocity of 40 m/s and an angle of 40 degrees above the horizontal. He needs to pass through a ring of fire 60 m away and land on a landing pad. Using the equations for projectile motion and splitting his velocity into horizontal and vertical components, the horizontal distance of the motion is found to be 31.57 m and the total distance is 100.67 m. The time taken for the whole motion is 5.13 seconds. To find the distance from the ground, the displacement formula is used and the total distance is found to be 160.62 m.
runningirl

## Homework Statement

Zandor is being shot out of his cannon (at a velocity of 40 m/s) at an angle of 40 degrees above the horizontal. He is planning to pass through a ring of fire (which is 60 m from where he starts) to the landing pad. How far is the ring of fire from the ground? How far is the landing pad from where he starts?

x=xo+vxo+at^2
y=yo+vyo+at^2

## The Attempt at a Solution

I tried finding time and got 6/4 seconds but I don't know if it's correct or not.

Well this is a projectile motion problem, so we can say that the velocity in the x direction is constant and the velocity in the y direction is changing correct?

Knowing this, for part A how long does it take Zandor to go 60m in the x direction? Can you then relate this to how high up he is?

For part B, how long is Zandor in the air? Can you relate this to how far he traveled in the x direction?

Hmm- the first things you should find are the horizontal and vertical distances of the motion.

1. Split the initial velocity into vertical and horizontal components so you can calculate the height and the horizontal distance of the motion.

2. Calculate the time taken for the whole motion.

I got 5.13s for the motion's total time taken.

Edit: adding to what fox said,

you might consider the 60m as a ratio of the whole horizontal distance.

i'm not i understand how to find the distances..
what equations am i supposed to use?

For part A)
There is no acceleration in the X direction correct? So the position formula for the x direction would be:
$$x_{f} = x_{0} + v_{x}t$$
We know what the final x position of the ring and his inital x position and velocity. So solve for the time it takes him to reach that x position, plug it into the position formula for the y direction and solve for y final

is vx=40?

how am i supposed to figure out part B because i don't know the vy, do i?

No his TOTAL velocity is 40. The angle he's being shot at is 40 degrees though, so use some trig and break the velocity into the x and y components

okay, i got part a to be 31.57 m and part b to be 100.67 m.
if anyone would like to check it i'd greatly appreciate it :)

Got the same for part A, but not for part B. I got 160.62m, looks like you subtracted the 60m from the starting point to the fire. Remember the question asks you the total distance to the landing pad from where he started.

The 4 equations I use for kinematics are:

s = vit + 0.5at2
s = 0.5(vi + vf)t
vf = vi + at
vf2 = vi2 - 2as

Apply whichever equation that has the variables you are given, and as I said earlier, try to think of the distance as the ratio:

60m / stotal = t60m / ttotal

P.S. I use s for displacement.

## 1. What is projectile motion?

Projectile motion is the motion of an object through the air that is influenced by gravity and air resistance. This type of motion follows a curved path called a parabola.

## 2. How is projectile motion different from regular motion?

Regular motion follows a straight path and is not affected by gravity. Projectile motion, on the other hand, follows a curved path and is influenced by gravity.

## 3. What is the formula for calculating projectile motion?

The formula for calculating projectile motion is:
- Horizontal distance (x): x = v0cosθt
- Vertical distance (y): y = v0sinθt - (1/2)gt2
- Time (t): t = 2v0sinθ/g
Where v0 is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

## 4. What factors affect projectile motion?

The factors that affect projectile motion are:
- Initial velocity: The speed and direction at which the object is launched.
- Angle of projection: The angle at which the object is launched.
- Air resistance: The force exerted by air on the object as it moves through the air.
- Gravity: The force that pulls the object towards the ground.
- Mass and shape of the object: Heavier and more aerodynamic objects will have different projectile motion than lighter and less aerodynamic objects.

## 5. How is projectile motion used in real life?

Projectile motion is used in many real-life situations such as:
- Sports: Projectile motion is used in sports such as baseball, football, and basketball to predict the trajectory of the ball.
- Fireworks: The motion of fireworks is an example of projectile motion, as they are launched into the air and follow a parabolic path.
- Space travel: The motion of satellites and spacecrafts in orbit around the Earth or other planets can be described using projectile motion.
- Projectiles: Projectile motion is used in military and defense systems to accurately aim and project missiles, rockets, and other weapons.

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