Projectile Motion from a Cliff: Solving for Initial Velocity and Launch Angle

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In summary, the problem requires more information in order to solve for the initial launch velocity and launch angle of the projectile. The given equations and data are not enough to uniquely define a solution. Additional information such as the time of flight or another measurement is needed to solve the problem.
  • #1
pkc111
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Homework Statement


A projectile fired up into the air from the top of a 75m high cliff hits the ground 500m out from the base.
Calculate the initial launch velocity (U), and launch angle (theta) of the projectile.


Homework Equations


1) v=u+at
2) v2=u2 +2as
3) s=ut+0.5at2


The Attempt at a Solution


Consider up to be positive direction.
Consider vertical component (y component) of motion for entire flight:
a=-9.8 m/s2
s=-75m
uy=Usin(theta)

Sub into Eqn 3:
-75=Usin(theta)t+0.5(-9.8)t2 #EQN A

Consider horizontal component (x component) of motion for entire flight:
a=0
s=500m
ux=ucos(theta)

Sub into Eqn 3:
500=ucos(theta)t #EQN B


Now comes the problem... I have created 2 equations (A,B), but with 3 unknowns (u, theta,t). I think I need another equation ?

This is REALLY bugging me, please help.
Thanks very much.
 
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  • #2
Your thinking is correct. You do need more information. The answer to this problem is not uniquely defined with the information that is given.
 
  • #3
OK thanks, but the book gives the answer as 65m/s at an angle of 40degrees to the horizontal.
Could it be that I need to create another equation from my data ??

Thanks
 
  • #4
As I said earlier, there are pairs of angles and initial speeds that give the same numbers. The numbers that are given by the problem do not uniquely define a solution. Try this:

Assume that the angle is 40o and that the initial speed is 65 m/s.
Solve your EQN B for the time of flight.
Plug the numbers in the right side of EQN A; you should get -75 m.

Now repeat but with an angle of 60o and initial speed 72.15 m/s and see what you get.

The answer to this problem is not unique unless some other quantity is given to remove the ambiguity. You have created all the equations that can be created from what is given. To get another equation, you need more data.
 
  • #5
Thanks kuruman I see your point.
 

What is a projectile?

A projectile is any object that is thrown or launched into the air and is subject to the force of gravity.

What is a cliff?

A cliff is a steep, vertical or nearly vertical rock face or slope, typically found near bodies of water.

What factors affect the trajectory of a projectile from a cliff?

The factors that affect the trajectory of a projectile from a cliff include the initial velocity, the angle of launch, air resistance, and the force of gravity.

How does the height of a cliff affect the distance a projectile travels?

The height of a cliff can greatly affect the distance a projectile travels. The higher the cliff, the longer the projectile has to travel horizontally before it reaches the ground, resulting in a longer distance traveled.

What is the formula for calculating the distance traveled by a projectile from a cliff?

The formula for calculating the distance traveled by a projectile from a cliff is d = (v^2 * sin(2θ))/g, where d is the distance, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

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