Formulas
What is the formula you should use to find horizontal displacement of a projectile?
dx = (vx)(t)
Define projectile
Objects given initial velocity but then move only under the force of gravity
A ball is thrown off the balcony of an apartment. The ball is thrown horizontally at 3 m/s and takes 1.2 seconds to reach the ground. How far from the balcony did the ball land? Show the formula, work, and answer with correct units.
dx = (vx)(t)
dx = 3m/s x 1.2s
dx = 3.6m
What is the value of vfy at then end of the projectile?
Opposite of viy
What type of trig function should you use when finding the vertical component?
Sine
vy = sine(theta)(v)
Define trajectory
The path followed by a projectile
A cliff diver jumps off the edge of a cliff at 7 m/s that is 78 meters high. How long does the diver take to reach the water? Show the formula, work, and answer with correct units.
t = √2dy/g
t = √(2)(-78)/(-9.81)
t = 3.99s
Describe the shape/path of projectile motion.
Parabolic shape
What type of trig function should you use when finding the horizontal component?
Cosine
vx = cosine(theta)(v)
Define inertia
Tendency of an object not to change its motion
A golf ball is hit from ground level at a velocity of 22 m/s at an angle of 77°. What is the vertical component, horizontal component, vfy and fiy? Show the correct formula, work, and answer with correct units.
vy = sine(theta)(v) vy = sin(77)(22) vy = 21.4
vx = cosine(theta)(v) vx = cos(77)(22) vx = 4.95
vy = viy viy = 21.4
vfy = opposite of viy vfy = -21.4
In what direction does gravity ONLY act?
Vertically
What formula do you use to calculate the time it took for the entire projectile? For maximum height what would you use for vfy? How else can you solve for time to maximum height?
t = vfy - viy / g
To calculate max height you use the same formula but use 0 for fvy.
You can divide the entire time it took for the projectile to reach the ground by half to find the time it takes to max height.
Define gravity
The universal force of attraction that pulls objects with mass toward one another (9.81 m/s2)
A football is kicked from ground level into a goal post that is 45 meters away. The vertical component is 4.7. What is the total time that the football is in the air? What is the time to max height? What do you notice about your two answers? Show the correct formula, work, and answer with correct units.
entire time:
t = vfy - viy / g t = -4.7-4.7/-9.81 t = 0.958s
max height:
t = vfy - viy / g t = 0-4.7/-9.81 t = 0.479s
max height is half of the entire time!
There is no _____________ in the horizontal direction.
Acceleration
What two formulas can you use to calculate maximum height? When would you use each formula?
dy = vfy2 - viy2 / 2g
use this one when you do not know time
or
dy = viyt + 1/2gt2
use this one if you do know time
Define FHS
Foothill High School
A basketball is shot into a hoop. The vertical component of the basketball is 16.4 the time it took for the ball to reach the hoop was 2.3 seconds. What is the max height of the basketball? Show the correct formula, work, and answer with units.
dy = viyt = 1/2gt2
dy = (16.4)(2.3) + 1/2(-9.81)(2.3)2
dy = 37.72 + -25.95
dy = 11.7m
In a vector diagram of projectile motion describe how vx and vy behave. Sketch a picture.
vx is constant (vector in the horizontal (direction (pointing to the right))
vy increases by 9.81 each time (vector in the vertical direction (pointing down))