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

In summary, a projectile is launched from a cannon at a target 1580 m away with an initial velocity at an angle of 24 degrees with the horizontal. The target is successfully hit. The acceleration of gravity is 9.8 m/s^2. The magnitude of the initial velocity is required, as well as the highest point of the trajectory and the time it takes to reach the target with no friction. Using relevant projectile motion equations, the initial velocity can be determined by solving for Vo in the range equation, which involves the time of flight and the angle of launch.
  • #1
Jimkatz809
8
0

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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  • #2
Collect the relevant equations for projectile motion from any source.
 
  • #3
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
 
  • #4
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
 
  • #5
Vo is not given
 
  • #6
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.
 

1. What is the formula for finding initial velocity with only distance, angle, and acceleration?

The formula for finding initial velocity with only distance, angle, and acceleration is v0 = √(d * g * 2 * sin(θ)) where v0 is the initial velocity, d is the distance, g is the acceleration due to gravity, and θ is the angle of launch.

2. Can you explain the significance of each variable in the formula?

Distance (d) is the length of the path traveled by the object, angle (θ) is the angle at which the object is launched, and acceleration due to gravity (g) is the rate at which objects fall towards the earth. These variables are necessary in the formula to calculate the initial velocity of the object.

3. Is this formula applicable for all types of motion?

No, this formula is specifically for calculating the initial velocity of an object launched at an angle (projectile motion) with only the given variables. It cannot be used for other types of motion such as uniform or non-uniform motion.

4. How accurate is this formula in determining the initial velocity?

This formula is accurate for calculating the initial velocity of an object in ideal conditions, where there is no air resistance or external forces acting on the object. In real-world scenarios, there may be slight variations due to external factors.

5. Are there any limitations to using this formula?

Yes, this formula assumes that the object is launched at an angle and that the acceleration due to gravity is constant. It also does not take into account air resistance or other external forces. Additionally, it may not be accurate for objects with complex trajectories or irregular shapes.

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