# Deriving Projectile Motion Equations

1. Jun 3, 2013

### rakeru

1. The problem statement, all variables and given/known data

A projectile is fired from ground level at time t=0, at an angle of θ with respect to the horizontal. It has initial speed V0.

Part A

Find the time it takes the projectile to reach its maximum height. Express in terms of V0, θ, and g.

Part B

Find the time at which the projectile hits the ground after having traveled through a horizontal distance, R. Express in terms of V0, θ, and g.

Part C

Find the maximum height attained by the projectile. Express in terms of V0, θ, and g.

Part D

Find the total distance R traveled in the x direction. Express in terms of V0, θ, and g.

2. Relevant equations

V=V0+at

y=y0+Vy0t+0.5ayt2

x=Vx0t

3. The attempt at a solution

For Part A, I did:

Vy=Vy0 + ayt

0=V0sinθ-gt

gt=V0sinθ

t=(V0sinθ)/g

For Part B I did:

y=y0+Vy0+0.5ayt2

0=0 + (V0sinθ)t- 0.5gt2

0.5gt2=(V0sinθ)t

gt2= (2V0sinθ)t

t= (2V0sinθ)/g

For Part C I did:

Vy2=Vy02+2ay

0=(V0sinθ)2-2gy

y= (V0sinθ)2/2g

For Part D:

x = x0 + Vx0t

x= V0cosθ × (2V0sinθ)/g

x= (V02sin2θ)/g

Did I do this correctly?? Or did I just mess up everything.. The one I'm really confused about is Part C.. I don't know if I could use the equation that I used..

2. Jun 3, 2013

All good.

3. Jun 4, 2013

### rakeru

Really!? So I am right.. I was told by someone that part C was wrong.. o_o

4. Jun 4, 2013

### haruspex

Checked it again... part C still looks right to me.