Question

please use Projectile simulator, for the Lab Projectile Motion in 2-D and answer question below

**14**. Solve for t. [Hint, you can factor one of
the variables.]

**15**. What is the smaller answer referring
to?

Given that your larger answer should be the time it takes to land,
use that in your x-position equation, i.e. rewrite your equation
for x, replacing t with what you got in #14.

**16**. How far does it travel in the x-direction
before it lands? Note you should still have θs involved.

The max distance reach on the X-displacement 163.27 (m) with the setting 40 m/s at 45-degree angle

Now finally, we have an equation for how far the ball travels purely as a function of the launch

angle θ! To wrap everything up, we need to consider what θ will give us a maximum value.

Looking at our equation, it seems like we might be right back to where we started, just trying to

plug in values to see what gives the highest value! However, we figure someone may have

thought about this before, so we consult our book of mathemagics, which tells us the following:

f will be at a maximum when sin(2θ) is at a maximum, as θ is the only variable in the equation.

**17.** What values does the sine function go in
between?

**18.** What angle causes the sine function to be
at this highest value?

**19.** If that angle is 2θ, then what would that
make θ?

Use the applet to check your answer does indeed give the launch angle that sends the projectile

the farthest.

**20**. What is the launch angle that makes a
projectile travel the farthest? How can you tell?

Answer #1

Use the simulation to answer the following questions.
- Open the PhET Projectile Motion Simulation (
https://phet.colorado.edu/en/simulation/projectile-motion) and use
it to answer the following questions:
1. For a given launch speed and no air resistance, what launch
angle causes the projectile to travel the furthest.
2. Turn on air resistance. Does air resistance influence the
angle you found in part 4? If so, how? (You may need to add quite a
bit of air resistance or set the mass...

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