Projectile motion

YOU MOSTLY NEED TO DO PRACTICE QUESTIONS

define projectile

object where only force is gravity

assumptions made in projectile motion

no air resistance, gravity is constant, there is no friction (if being rolled off a cliff), no rotational motion, etc

how to solve projectile qs

consider horizontal and vertical components separately —> only common measurement is time

—> horizontal = constant velocity (no acceleration)

—> vertical = constant acceleration down

DIRECTION IS VERY IMPORTANT

equations

key notes:

• at max point vy=0 but vx is constant

• for a full parabola, time of flight is 2 times the time to max height —> due to symmetry

• use the equations to solve for any unknowns

• gravity is -9.8m/s/s

• can decompose launch angle to x and y

u = initial v= final

NOTE: IF A BALL IS DROPPED VERTICALLY WHILST A BALL IS THROWN HORIZONTALLY, (when Ux is same for both), they will land at the same time

Influence of variable on projectile

• Ux

• Uy

• Sy

• g

• U

• launch angle

• determines range + shape

• determines max height + time of flight

• same Uy, they have the same Vy

  • the same time of flight, the same max height (assuming that the projectile was dropped from the moving object)

  • are always in line with each other vertically (when the projectile hits the ground, the object that dropped it will be directly above it)

• Increasing acceleration decreases the range, and max height, and time of flight

• Increasing the launch velocity increases maximum height, time of flight, and range

• angle:

  • Optimum Launch angle for range is 45

  • Optimum launch angle for max height is 90°

proof for optimum range

use v=u+at for vertical components, rearrange for t

sub t=(v-u)/a in for Sx=Ux t

v and u are the same quantity but opposite signs so = -2v

use double angle rule so 2sinWcosW = sin2W, and sin2W greatest when 2W=90 W=45

questions involving stroboscope

gaps = time interval

use scale measure distance and fine Ux —> convert scale to real life

no. of images missing = distance of missing images ÷ distance between one image