# Finding Range, Max Height and Speed of Projectile

## 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.
A) 625*sqrt(3)/4 ft
B) 625/16 ft
C) 100 ft/s

Related Introductory Physics Homework Help News on Phys.org
How did you obtain those answers?

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

~Lyuokdea

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

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 forumla for max height of projectile.
Using given data,
y=38.86 ft ...(Max height)

Since, there is no acceleration along x-axis,
vx=v0cosA+(0)t
The net y-displacement of projectile is zero
vy2=(v0sinA)2-2g(0)
vy=v0sinA
The components of final velocity are same as that of initial velocity, hence, the velocities must be equal. Therefore,
v=100 ft/s