Find initial Velocity with only distance, angle, and acceleration.

AI Thread Summary
To find the initial velocity of a projectile launched from a cannon at a 24° angle to hit a target 1580 m away, the relevant equations of projectile motion must be applied. The horizontal and vertical components of the initial velocity can be expressed as Vox = VoCos(θ) and Voy = VoSin(θ). By using the equation for range R = Vox * t and the time of flight derived from vertical motion, the initial velocity can be solved. Additionally, the maximum height of the trajectory can be calculated using the vertical motion equations. The problem emphasizes the need to derive time and initial velocity from the given parameters without friction.
Jimkatz809
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Homework Statement


A cannon sends a projectile towards a target
a distance 1580 m away. The initial velocity
makes an angle 24◦ with the horizontal. The
target is hit.
The acceleration of gravity is 9.8 m/s2 .
What is the magnitude of the initial veloc-
ity?
Answer in units of m/s.

How high is the highest point of the trajec-
tory?
Answer in units of m.

How long does it take for the projectile to
reach the target? (Assume no friction)
Answer in units of s.


Homework Equations





The Attempt at a Solution

 
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Collect the relevant equations for projectile motion from any source.
 
Ive spent about 2 hours trying and trying this problem but i can't figure out the answers.
The equations i used were
Vox=VoCos0o
Voy=VoSin0o
V^2=Vo^ plus 2a(x-xo)
V=Vo plus at
 
Since there is no acceleration in the x direction, vox remains constant.
Using the last equation you can find the time to reach the maximum height. Here V = 0, Voy = Vosinθ and a = g.
Double that time is the time of flight t.
Range of the projectile R = Vo*cosθ* t
 
Vo is not given
 
Jimkatz809 said:
Vo is not given
First of all find t in terms of Vo, sinθ and g. substitute this value in the expression for R and solve for Vo.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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