If a 20 kg artillery shell is launched vertically with a velocity of 37 m/s, how high in meters does it rise? use the acceleration due to gravity as 9.8 m/s2.
or-
how do you calculate projectile motion? what are the formulas?

1. 69.8 m

The vertical motion of the shell is a uniformly accelerated motion, with constant acceleration towards the ground (acceleration due to gravity).

At the point of maximum height, the velocity of the projectile is zero:

v = 0

So we can find the maximum height by using the equation:

where

u = 37 m/s is the initial velocity

d is the maximum heigth

Solving for d,

2)

A projectile motion consists of two separate motions:

- A uniform motion along the x-direction, with constant velocity given by

where is the initial velocity, and the angle of launch

- A unformly accelerated motion along the y-direction, with initial velocity

and constant acceleration

(acceleration due to gravity) towards the ground.

The horizontal position of the projectile at time t is given by

while the vertical position is given by

where is the initial height of the projectile.