Calculate the velocity of the projectile

[Fadi A.Saif]

Homework Statement

A stone was thrown with initial velocity of 100 m/s. Calculate the velocity of the projectile at 10 m of height. (Consider g=10m/s^2, and neglect the effect of air molecules)

Homework Equations

where's the error in the following sollution?

The Attempt at a Solution

Vr= sqrt((Vx)^2+(Vy)^2)...(1) (Resultant velocity).
Vx= Vi cos(a)...(2)
Vy=Vi sin(a)+(-2gy)...(3)
sub. (2)& (3) in (1)
Vr = sqrt(Vi^2 (cos(a))^2+Vi^2 (sin(a))^2+(-2gy)); taking Vi as a common factor, and sqrt of both sides; we get
Vr = sqrt(Vi^2-2gy) then we proceed by applying the given data from the problem

 

[kuruman]

The error is right here

Vy=Vi sin(a)+(-2gy)

This equation is not dimensionally correct.

 

[Fadi A.Saif]

Thanks Kuruman... so I believe it should be like this
Vy^2= Vi^2 (sin(a))^2 - 2gy.

 

[kuruman]

That's more like it.