Question

Define the term projectile. Derive expressions for the time taken by a projectile to
reach the highest point and the maximum height attained.​

Answer 1

A projectile is an object upon which the only force acting is gravity.There are a variety of examples of projectiles. An object dropped from rest is a projectile (provided that the influence of air resistance is negligible). An object that is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible). And an object which is thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible). A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity. Simply saying "Projectile motion is the motion of an object who's path is affected by the force of gravity"

refer the diagram below .  

Hmax = u²sin²∅/2g  

Time required : t =  U sin ∅ / g  

Explanation:

et a projectile moves with u velocity which inclined with horizontal ∅ angle .  

then,  

velocity vector after t time (V)

V = Vx i + Vy j  

V = ucos∅ i + (usin∅ -gt) j  

at maximum height velocity of projectile have only x -components exist .e.g  

Vx =ucos∅  

use , Vy² = Uy² + 2ay.Y  

or projectile  

Vy at maximum height = 0

Uy = usin∅  

ay = -g                                          // taking uward direction as +ve .

Y = maximum height  

 

put this ,  in Vy² = Uy² + 2ay.Y  

0 = (usin∅)² -2gHmax

Hmax = u²sin²∅/2g  

to calculate the time for reaching

Vy = Uy +g t

since v = 0 , at highest point

Uy = U sin ∅

0 = U sin ∅ - g t

t =  U sin ∅ / g