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

[hechen]

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

 

[gneill]

The projectile's trajectory is not a straight line. What shape is it? What equations govern the motion in the X and Y directions?

 

[hechen]

There were no more information given then what I posted. Which is puzzling.

 

[gneill]

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.

 

[hechen]

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.

 

[gneill]

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.