## Pages

### 2.1 Kinematics (Projectile motion)

Projectile motion: "Projectile motion is a form of motion in which an object or particle (called a projectile) is thrown near the earth's surface, and it moves along a curved path under the action of gravity only."-wikipedia

The way how we are going to understand the projectile motion is by directly solving the problem. Now given the above projectile motion, how do you approach solving for different quantities you would like to find. For instance I could ask,
1.How high does the ball reach from the current position?
2.What is the range of the ball? or in other words how far does ball goes before it hits the ground?
3.What is the vertical component of velocity upon hitting the ground?
Before solving these question let's first look at the given in the problems,

(This diagram is only for intuition)
SOLn:
• acceleration due to gravity=$\pm 9.8m/s^{2}$
• projectile velocity=30m/s
• angle of projectile=60 degree
• ball above the ground=9m
• maximum height from the current position=?
• range=?
• vertical component velocity of the ball hitting the ground=?
$v_{x}=30 \cos (60)$ =15m/s
$v_{y}=30 \sin (60)$ = 25.981m/s
$g =-9.81m/s^{2}$
-height reached by the ball from current position= $({v^{2}-u^{2}})/{2a}$ =34.4m
-time to reach=2.648s
-actual height from the ground=43.404m
-time to reach ground= $\sqrt {2s/g}$=2.975s
-vertical velocity component hitting to ground=29.182m/s
-range=84.345m(it's important to remember that there's no horizontal forces acting therefore the horizontal velocity remains same)

Here a similar problem shown in the video.

If you are not sure of the kinematics five magic formula click here to revise.

If you are absoloutely new to projectile motion then this video will help you,