How to find initial velocity given distance and angle

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Homework Help Overview

The problem involves determining the initial velocity of a projectile launched at an angle of 20° to hit a target located 3 km away. The context is rooted in projectile motion, specifically focusing on the relationships between distance, angle, and initial velocity.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss isolating time from the motion equations and question the implications of negative values in calculations. There are mentions of using trigonometric functions to resolve components of the initial velocity and considerations about the vertical position of the projectile when it returns to the ground.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the equations involved. Some guidance has been offered regarding the use of the vertical motion equation and the significance of the projectile's position when it impacts the ground. Multiple interpretations of the problem setup are being examined.

Contextual Notes

Participants note the acceleration due to gravity as -9.81 m/s² and express concerns about the number of unknowns in the equations. There is also a clarification regarding the vertical distance when the projectile reaches the ground.

tsukuba
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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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Some hints: Draw the diagram and then use the formula. What do you know about the x-distance and y-distance?
 
I have to multiply it by cos20 and sin 20
 
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
 
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.
 
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:
0=v_0\sin(20)t-\frac{9.8}{2}t^2
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
 
instead of the 0 wouldn't i have the distance of 3km?
 
here is the question and the diagram
mec.png
 
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.
 

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