Question

If I have time, displacement, and angle, how can I calculate the overall velocity of an object in projectile motion? As in thrown in an arc.

Answer 1

Like, if I know displacement = 55 m, time = 12 s, angle of throw = 45 degrees, and acceleration = gravity, can I find the velocity over an arc?

Answer 2

you better split it into two components.. and treat each component seperately

Answer 3

Can you explain more?

Answer 4

ok.. lets see..



so i believe you want the velocity somewhere like i have marked..

consider the motion in vertical and horizontal seperately they live a life of their own

lets say vertical for now

what is the initial velocity well its using(theta) [in your example u sin(45)]
final velocity!? you wanna find out
but you know how much time (in your example 12s)
and also you know what is the acceleration (g)
use appropriate equation of motion to develop an equation.. you ll get an equation with u and v as variables

now consider horizontal motion
in horizontal motion the velocity is a constant
hence all you have to use is velocity(u cos(45)) = displacement / time
since you know displacement (55m) and time(12s)
you know what is the horizontal velocity.. and yes the horizontal initial velocity is equal to the horizontal final velocity.. cause the velocity ALWAYS remains same in horizontal.. no acceleration

so now you find u from the above equation

plug it in the first equation and get v

so you now have the final velocity in the VERTICAL direction and in the HORIZONTAL direction

so get the resultant!