# Physics - Projectile Motion

This is going to be hard to explain, but I did an experiment on projectile motion and we had to lauch a marble from 0 degrees to 90 degrees in a 5 degree interval using a projectile launcher with the same velocity each time.
We had to investigate the angle which gave the greatest range, and I graphed the results. The graph looked like the letter M, where range was on the y-axis, and the degree of launch was on the x-axis. The graph increased until 30 degrees, then there was a slight drop, then it peaked again at 50 degrees.

THe question asked Use your graph to determine the relationship between the range of a projectile and pairs of launch angles, eg 15 degrees and 75 degrees

I would think the answer would be a quartic relationship by looking at the graph of some sort, but then again we haven't learnt quartic yet. I think it could be also a quadratic realtionship because projectiles move in a paranolic matter, and I think my teacher mentioned it once before.

1. 👍 0
2. 👎 0
3. 👁 51
1. Ignoring the friction of the air, the parabola is what it should do.
The 50 degrees is not bad. I do not know how your setup worked but suspect that anywhere from 30 to 60 degrees might look good with the inevitable uncertainties in launch speed.
If you did it with math instead of experiment you would come up with 45 degrees.
u = Uo forever in the horizontal direction
v = Vo - 9.8 t in the vertical direction with initial speed Vo up and time t and acceleration of gravity = 9.8 m/s
tan A = Vo/Uo tangent of launch angle to horizontal
s^2 = Uo^2+Vo^2 = speed at launch
x = Uo t distance down range
y = Vo t - 4.9 t^2
so
t = x/Uo
y = Vo x/Uo - 4.9 x^2/Uo^2
NOTICE that is a parabola
the projectile comes back to ground when y = 0 so
for range
4.9 xmax^2/Uo^2 = Vo x/Uo
4.9 xmax = Vo Uo
xmax = Vo Uo / 4.9
remember tan A = Vo/Uo so Vo = Uo tan A
so xmax = Uo^2 tan A/4.9
for a given s, what is the maximum range?
Uo^2 = s^2 cos^2 A
so xmax = s^2 cos^2 A (sin A/cos A)
= s^2 sin A cos A
SO
our maximum range is where sin A cos A is maximum
Now you can graph that or use calculus
graphing sin A cos A is hard on the computer so I will use calculus.
f(A) = sin A cos A
dF/dA = sin A (-sin A) + cos A (cos A)
for max or min df/dA = 0 so
sin^2 A = cos^2 A
that is true when A = 45 degrees
So you should have found maximum range when A is 45 degrees which is why I said 50 degrees was pretty good.

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### physics

i don't understand the projectile motion...my teacher said...it's a motion of a body confined to a vertical plane, perpendicular to Earth's surface... I don't get it, can anyone explain to me clearly???? plzzzzz....THX!!!! If your

asked by Katrina on November 29, 2006
2. ### Science - Physics

When a projectile is fired horizontally, which of the components of its motion is (A) motion at constatnt speed (B) uniformly accelerated motion (C) If the initial velocity of the projectile is increased, what effect will this

asked by Nicole on December 6, 2006
3. ### physics

A mass makes a projectile motion on a table (like the one in the projectile motion experiment) with inclination angle of the table as α=6o. The initial velocity and the initial angle are is 100 cm/s and 30 deg. respectively. What

asked by anonymous on December 21, 2012
4. ### Science Physics

Projectile motion problem. The maximum range for a projectile is achieved when the projectile is fired at 45 degrees. This is true if the launch starts and ends at the same altitude. What about if you fire at a target at a lower

asked by Alex on February 1, 2018
5. ### Physics

A projectile is launched at an angle of 34.0o above the horizontal. The projectile has a mass of 1.50 kg and is given an initial speed of 20.0 m/s. a) What is the initial kinetic energy of the projectile? b) By how much does the

asked by John on May 30, 2014
6. ### Science

My assignment is to make an experiment to investigate the effect different forces have on an object’s motion. And this should test at least one of the laws of motion. Now all I ask is an example of an experiment I could do. I'm

asked by Lexi on October 6, 2016
7. ### Physics

Which of the following statements about projectile motion is not correct? a)The acceleration is constant and in one direction. b)The only force is gravity. c)In projectile motion, the motion can be broken down into perpendicular

asked by Lewis on October 14, 2012
8. ### physics

True/False (#1 only) 1)The horizontal motion of a horizontally launched projectile affects its vertical motion. False 2)The path of a projectile through space is called its. Trajectory

asked by Jon on April 1, 2008
9. ### Physics

Q Exactly 2.7s after a projectile is fired into the air from the ground ,it is observed to have a velocity v = (8.8i+4.5 j) m/s where the x-axis is horizontal and the y axis is positive upward . a)Determine the horizontal range of

asked by Nikitha on September 1, 2012
10. ### Physics - rojectile Motion (check pls)

Imagine that you are solving a problem in projectile motion in which you are asked to find the time at which a projectile reaches a certain vertical position. when you solve the problem you find out two different positive values

asked by Shaila on August 21, 2010

More Similar Questions