(adsbygoogle = window.adsbygoogle || []).push({}); 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 V_{0}.

Part A

Find the time it takes the projectile to reach its maximum height. Express in terms of V_{0}, 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 V_{0}, θ, and g.

Part C

Find the maximum height attained by the projectile. Express in terms of V_{0}, θ, and g.

Part D

Find the total distance R traveled in the x direction. Express in terms of V_{0}, θ, and g.

2. Relevant equations

V=V_{0}+at

y=y_{0}+V_{y0}t+0.5a_{y}t^{2}

x=V_{x0}t

3. The attempt at a solution

For Part A, I did:

V_{y}=V_{y0}+ a_{y}t

0=V_{0}sinθ-gt

gt=V_{0}sinθ

t=(V_{0}sinθ)/g

For Part B I did:

y=y_{0}+V_{y0}+0.5a_{y}t^{2}

0=0 + (V_{0}sinθ)t- 0.5gt^{2}

0.5gt^{2}=(V_{0}sinθ)t

gt^{2}= (2V_{0}sinθ)t

t= (2V_{0}sinθ)/g

For Part C I did:

Vy^{2}=Vy0^{2}+2ay

0=(V_{0}sinθ)^{2}-2gy

y= (V_{0}sinθ)^{2}/2g

For Part D:

x = x_{0}+ V_{x0}t

x= V_{0}cosθ × (2V_{0}sinθ)/g

x= (V0^{2}sin2θ)/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..

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# Deriving Projectile Motion Equations

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