How to find initial velocity given distance and angle

In summary: What is the y position of the projectile when it hits the ground?In summary, a projectile is fired with an initial velocity Vo at an angle of 20° with the horizontal. The required value of Vo for the projectile to hit point b, 3 km away, can be determined by isolating time (t) from the formula y=(Vy)o t + 1/2 a t^2. However, since the acceleration (a) is a negative number, this results in a square root of a negative number, which is not possible. Instead, the equation 0=v_0\sin(20)t-\frac{9.8}{2}t^2 can be used to solve for t, taking into
  • #1
tsukuba
47
0

Homework Statement


A projectile is fired with initial velocity Vo at an angle of 20° with the horizontal. Determine the required value of Vo if the projectile is to hit point b.
point b is 3 km away.


Homework Equations


y=(Vy)o t + 1/2 a t^2


The Attempt at a Solution


i tried isolating time(t) from the above formula which gave me square root of 2y/a but i can't take the square root of a negative number that bring the acceleration
 
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  • #2
Some hints: Draw the diagram and then use the formula. What do you know about the x-distance and y-distance?
 
  • #3
I have to multiply it by cos20 and sin 20
 
  • #4
Hi Tsukuba. Welcome to Physics Forums.

What is the value of y when the projectile reaches the ground again? What is the acceleration "a" in your equation for y? Can you use your equation for y to figure out how much time the projectile is in the air?

Chet
 
  • #5
hello and thank you.

a=-9.81 m/s^2
I can use the equation because i would have 2 unknowns, that being the initial velocity and time. Like i said I tried isolating time and the formula i get is square root of 2x/a and i can't take the square root of a negative number.
 
  • #6
tsukuba said:
hello and thank you.

a=-9.81 m/s^2
I can use the equation because i would have 2 unknowns, that being the initial velocity and time. Like i said I tried isolating time and the formula i get is square root of 2x/a and i can't take the square root of a negative number.
As I see it, your equation for the y direction is going to be:
[tex]0=v_0\sin(20)t-\frac{9.8}{2}t^2[/tex]
Is this in agreement with your assessment? If so, you can solve this equation for t by factoring the right hand side, and discarding the root at t = 0. In terms of v0, what do you get for t?

Chet
 
  • #7
instead of the 0 wouldn't i have the distance of 3km?
 
  • #8
here is the question and the diagram
mec.png
 
  • #9
tsukuba said:
instead of the 0 wouldn't i have the distance of 3km?
We are talking about the y direction here, not the x direction. When the projectile hits the ground, y = 0.
 

1. How do I find the initial velocity given distance and angle?

To find the initial velocity given distance and angle, you can use the following formula: V0 = √(g*d/sin(2θ)), where g is the acceleration due to gravity (usually 9.8 m/s^2), d is the distance traveled, and θ is the launch angle.

2. Can I use this formula for any type of projectile motion?

Yes, this formula can be used for any type of projectile motion, as long as the initial velocity is being launched at an angle.

3. What units should I use for the distance and angle?

The units for distance should be consistent with the units used for acceleration due to gravity (usually meters). The angle should be in radians, so if you have degrees, you will need to convert them to radians first.

4. What if I don't know the distance traveled?

If you don't know the distance traveled, you will not be able to calculate the initial velocity using this formula. You will need to have either the distance or the initial velocity to solve for the other.

5. Is there a more accurate way to calculate initial velocity?

Yes, there are other methods to calculate initial velocity using different variables such as time and displacement. However, the formula provided is a commonly used approximation and is accurate enough for most situations.

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