Download the projectile motion physics simulation from the PhET website: http://

Question

Download the projectile motion physics simulation from the PhET website: http://phet.colorado.edu/en/simulation/projectile-motion.

A. What happens when you fire your projectile at the same velocity, but a different angle? What happens when you fire your projectile at the same angle, but a different velocity? Explain this behavior using your knowledge of vector components.

B. What angle allows your projectile to stay in the air for the longest amount of time? Again, how does this make sense in the context of vector components?

C. Select a different type of projectile with a different mass. Keep your angle and firing velocity the same, and fire the new projectile. How does the trajectory of the new projectile compare to that of the old one? Is this a surprising result? Explain your answer by referencing the basic equations of motion with constant acceleration and/or Newton’s laws.

Explanation / Answer

A) consider initial velocity is v at angle @.

then in vertical:

initial vertical velocity = v sin@

a = - g

finally it come to same vertical position. (same level)

using d=ut + at^2 /2

0 = v sin@ t - gt^2 /2

t = 2v sin@ / g

v is same but@ is different then sin@ will also be difference .

so both projectile will have unequal time.

for maximum height.

vf^2 - vi^2 = 2ad

0^2 - (v sin@)^2 = 2(-g)(H)

H = v^2 (sin@)^2 / 2g

v is same but@ is different then sin@ will also be difference .

so both projectile will have unequal maximum height.

for range:

R = Vx* t = (v cos@) (2 v sin@ / g)

R = v sin(2@) / g

v is same but@ is different then sin2@ will also be difference .

so both projectile will have unequal range.

but 2@ can be inbetween 0 to 180 deg.

hence there will be two theta which will have same sin@ value.

sin(2@) = sin(180 - 2@')
@ = 90 - @'

angle that follow this relation will have same range.

at different velocity all three quantity will be different.

B) T = 2vsin@ / g

T will be max when sin@ is max,

so @ = 90

(when projectile is fired vertically, it have all velocity in vertical and it will have

maximum height and so maximum time.)

C) all terms are independent of mass.

hence changing mass willl not affect anything./

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