Projectile Motion, with only Displacement and Angle Known.

In summary, by breaking up the motion into x and y components and using equations for acceleration and displacement, we can find a relationship between initial velocity and time. By also considering the fact that horizontal speed remains constant, we can further narrow down the relationship between initial velocity and time. This allows us to solve for the initial velocity of the projectile.
  • #1
n72.75
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Homework Statement


A projectile is fired at an angle of 35° and lands 88.5 Meters Down Range.
Assume no air resistance, and a gravatational acceleration of 9.80665 M/S2

I can get as far as the trig, but it doesn't seem like there is enough information to find time or velocity.

Find Initial Velocity Of the Projectile.

Homework Equations


a = [tex]\frac{(V f - V i) }{ t }[/tex]
s = V i + [tex]\frac{1}{2}[/tex] at 2

The Attempt at a Solution



See Attachment.
 

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  • #2
Break up the motion into x&y components.

Since you know the distance, you can write an equation linking Vi and T (total time). Similarly because horizontal speed doesn't change, you can write an equation linking Vi and N=T/2.

Now, what happens when projectile is halfway there (with respect to the y-component of speed)?
 
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  • #3


I would first clarify that the given information is not enough to solve for the initial velocity of the projectile. In order to do so, we would need to know either the time of flight or the final velocity of the projectile. Without this additional information, we cannot accurately determine the initial velocity.

However, we can use the given information to make some general observations about the motion of the projectile. We know that the projectile has a displacement of 88.5 meters in the horizontal direction and we can assume that it has a displacement of 0 meters in the vertical direction (since it starts and ends at the same height). We also know the angle at which it was fired, which can help us determine its initial velocity in the horizontal and vertical directions.

Using trigonometry, we can determine the initial horizontal velocity (Vx) by using the cosine function: Vx = Vcos(35°). Similarly, we can determine the initial vertical velocity (Vy) by using the sine function: Vy = Vsin(35°). However, without knowing the value of V, we cannot solve for Vx or Vy.

In conclusion, while we can make some general observations about the motion of the projectile, we cannot accurately determine its initial velocity without additional information. It is important to always have enough information and to carefully consider the variables involved when solving for unknowns in a scientific problem.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and moves along a curved path due to the influence of gravity.

2. How is projectile motion calculated?

Projectile motion can be calculated using the equations of motion, which take into account the initial velocity, angle of projection, and acceleration due to gravity.

3. What is the importance of knowing only the displacement and angle in projectile motion?

Knowing only the displacement and angle in projectile motion allows us to determine the trajectory of the object and predict its future position and velocity.

4. Can projectile motion be affected by other forces besides gravity?

Yes, projectile motion can be affected by other forces such as air resistance or wind, which can alter the trajectory and speed of the object.

5. How does the angle of projection affect the range of a projectile?

The angle of projection has a significant impact on the range of a projectile. The greater the angle, the farther the projectile will travel, with the optimal angle for maximum range being 45 degrees.

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