Kinematics: Angled Projectile Launch

In summary, the conversation discusses finding the initial velocity of a projectile coming out of a cannon at a 20° angle. The equation d = (Vi)(t) + 1/2(a)(t)^2 is used to split the question into x and y components and solve for both. There is a mistake made in assuming v0y is 0, and the correct answer is found to be 44.5 m/s after correcting the algebra. The conversation also discusses the use of two equations to find v0x and v0y, and suggests eliminating t and finding v0x explicitly.
  • #1
SlooM
3
0

Homework Statement


Determine the initial velocity of the projectile as it comes out of a cannon at a 20° angle.


Homework Equations


d = (Vi)(t) + 1/2(a)(t)^2


The Attempt at a Solution


I've split the question into both x and y components and solved for both using the equation above. Although I'm honestly unsure if I'm doing this correctly, would like some verification on my answer and point out any mistakes. Much appreciated! (Image below)

http://imgur.com/pPWO2jG
 

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  • #2
Hi SlooM,

Are you sure v0y is 0 in the first equation that you've used to find t?
 
  • #3
Ah, I think that may have been my mistake which is kind of why I look at it and it doesn't make sense. I just put 0 for v0y and assumed it canceled that half of the equation. What would I put though, I feel like I don't have enough variables and am super confused.
 
  • #4
In addition to what Sunil has stated, there was also an algebra mistake at the end preventing you from getting the correct answer.

[tex]\cos\theta = \frac{v_x}{v_i}[/tex]

to

[tex](cos\theta)v_x = v_i[/tex]

instead of

[tex]v_i =\frac{v_x}{cos\theta}[/tex]


An easier way to do this problem it to remember that your x-component of velocity already has a cosine term in it. So once you solve for time you can simply say

[tex]x(t) = V_otcos\theta[/tex]
 
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  • #5
Oh! I can't believe I didn't see that. So I redid the algebra at the end and got 44.5 m/s but are my calculations in the previous x and y calculations correct? I keep second guessing myself :/

I'm a rookie at physics but trying to improve. I appreciate all of your help and it means a lot.
 
  • #6
SlooM said:
Oh! I can't believe I didn't see that. So I redid the algebra at the end and got 44.5 m/s but are my calculations in the previous x and y calculations correct? I keep second guessing myself :/

I'm a rookie at physics but trying to improve. I appreciate all of your help and it means a lot.

Hey we are all rookies :smile:

We get two equations right?

[itex]-1.5= v_{0y}t + \frac{g}{2}t^2[/itex]
[itex]23=v_{0x}t[/itex]

All we have to do is eliminate t. Moreover, v0x and v0y are related. So, you should be able to find v0x explicitly (and hence v0y).

Could you check you answer again? I seem to be getting something different.
 

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause that motion. It involves analyzing the position, velocity, and acceleration of an object over time.

2. What is an angled projectile launch?

An angled projectile launch is when an object is launched at an angle from the horizontal. This type of motion can be seen in activities such as throwing a ball or shooting a projectile from a slingshot.

3. What are the key variables in kinematics?

The three key variables in kinematics are position, velocity, and acceleration. Position is the location of an object, velocity is the speed and direction of an object's motion, and acceleration is the rate at which an object's velocity changes.

4. How is an angled projectile launch different from a vertical launch?

A vertical launch is when an object is launched straight up or straight down. In an angled projectile launch, the object is launched at an angle from the horizontal. This changes the direction and speed of the object's motion.

5. What is the equation for calculating the range of an angled projectile launch?

The equation for calculating the range of an angled projectile launch is R = (v² * sin(2θ)) / g, where R is the range, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. This equation assumes a flat surface and no air resistance.

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