Finding Range, Max Height and Speed of Projectile

[jheld]

Homework Statement

A projectile is fired with an initial speed of 100 ft/s and angle of elevation Pi/6 (30 degrees).
Find:
A) the range of the projectile (along the x-axis)
B) the maximum height reached
C) the speed at impact

Homework Equations

Vf^2 = Vi^2 +2a*s
Vf = Vi + a*t
Sf = Si + Vo*t + (1/2)a*t^2
(where S is any coordinate axis)

The Attempt at a Solution

I have the answers from the answer key (this is a review), and I can't seem to get any of it right.
I found s (max height) (not S), to be 127.551 seconds.
I found t = 10.2 (from launch to landing)
I found range = 883.346.

I know this isn't a hard problem, but for some reason I cannot solve it.
The answers are:
A) 625*sqrt(3)/4 ft
B) 625/16 ft
C) 100 ft/s

 

[Lyuokdea]

How did you obtain those answers?

Try separating the equations for position into the x and y components.

~Lyuokdea

 

[jheld]

Vf = 0 (on the way up)
0 = 100^2*sin(30)^2-2(9.8)s
solving for s gives = 127.551 ft.

for time on the way up:
127.551 = 0 + 100sin(30)t - 4.8t^2
solving for t gives = 5.1 seconds

xf = 0 + 100cos(30)(5.1)2
= 883.346

I didn't try finding the impact speed because the other two answers were wrong.

 

[PhanthomJay]

The problem velocity is given in units of feet per second, not meters per second. Check out your value of 'g'.

 

[ajinx999]

There's no acceleration along x-axis. The acceleration due to gravity acts only along the -y axis. 'A' implies the angle of projection.
Assuming the projectile is fired from the origin,
x=v₀cosAt+0.5(0)t²
t=x/v₀cosA
The net y-displacement of the projectile is zero, since the projectile returns on x-axis.
(0)=v₀sinAt-0.5at²
Substituting t,
x=v₀²sin(2A)/g
This is the general formula for range of projectile.
Using given data,
x=269.20 ft ...(Range)

At the max height, the y-velocity of projectile is zero.
(0)=(v₀sinA)²-2gy
y=(v₀sinA)²/2g
This is the general formula for max height of projectile.
Using given data,
y=38.86 ft ...(Max height)

Since, there is no acceleration along x-axis,
v_x=v₀cosA+(0)t
The net y-displacement of projectile is zero
v_y²=(v₀sinA)²-2g(0)
v_y=v₀sinA
The components of final velocity are same as that of initial velocity, hence, the velocities must be equal. Therefore,
v=100 ft/s