Solve Projectile Angle Homework: Range 7x Height, Flat Landscape

In summary, in order to find the angle of launch for a projectile with a range seven times larger than its height, one must use the relationship between the x and y components of the initial velocity. Assuming that the components are vx and vy, the angle can be calculated using atan(vy/vx). The expressions for the maximum height and range can be used to determine the relationship between vx and vy in order to satisfy the given conditions.
  • #1
hechen
6
0

Homework Statement


This is all that is given:
If the range of a projectile's trajectory is seven times larger than the height of the trajectory, then what was the angle of launch with respect to the horizontal? (Assume a flat and horizontal landscape.)

Homework Equations



X = 7y

Y= Y

Arctan (Y/X)

The Attempt at a Solution



Arctan (1/7) ~ 8.13 deg

This answer was wrong according homework website I'm using
 
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  • #2
The projectile's trajectory is not a straight line. What shape is it? What equations govern the motion in the X and Y directions?
 
  • #3
There were no more information given then what I posted. Which is puzzling.
 
  • #4
hechen said:
There were no more information given then what I posted. Which is puzzling.

The only additional information required is the assumption that the projectile is moving under the influence of gravity near the Earth's surface. So acceleration is g in the vertical (Y) direction.
 
  • #5
I would then need to know time or was way to figure out time which is not possible in this case.
"If the range of a projectile's trajectory is seven times larger than the height of the trajectory, then what was the angle of launch with respect to the horizontal? (Assume a flat and horizontal landscape.)"
If the movement here is not linear the angle of the projectile depends on time.
 
  • #6
You can work with symbols rather than numbers. You're given a ratio of two distances that occur at specific times in a projectile's lifetime (max height and range), and you should be able to derive expressions for each. Also, the only angle you're interested in is the one that occurs at the instant of launch.

I'll give you a hint. The launch angle is related to the x and y components of the initial velocity. If you assume that the components are vx and vy, then the angle is atan(vy/vx). So what you're aiming for is the relationship between vx and vy in order to satisfy the height-range requirement. I'd suggest finding expressions for the maximum height and the range as functions of vx and vy.
 

1. What is the formula for calculating the range of a projectile on a flat landscape?

The formula for calculating the range of a projectile on a flat landscape is Range = 7x Height. This means that the range is equal to 7 times the height of the projectile.

2. How do you determine the angle of projection for a given range and height?

The angle of projection can be determined by using the inverse trigonometric function of tangent, also known as arctan. The formula is Angle of Projection = arctan(Range/Height).

3. Can the range of a projectile be greater than its height when projected on a flat landscape?

Yes, it is possible for the range of a projectile to be greater than its height when projected on a flat landscape. This can happen when the angle of projection is greater than 45 degrees.

4. How does air resistance affect the range of a projectile on a flat landscape?

Air resistance can decrease the range of a projectile on a flat landscape because it opposes the motion of the projectile. This means that the projectile will lose velocity and therefore have a shorter range than if there was no air resistance.

5. Is the formula for calculating the range of a projectile on a flat landscape applicable to all situations?

No, the formula Range = 7x Height is only applicable to situations where air resistance is negligible and the landscape is completely flat. In real-world scenarios, other factors such as wind, air resistance, and varying landscapes can affect the range of a projectile.

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