Please help projectile motion question

[runningirl]

please help :) projectile motion question!

Homework Statement

Zandor is being shot out of his cannon (at a velocity of 40 m/s) at an angle of 40 degrees above the horizontal. He is planning to pass through a ring of fire (which is 60 m from where he starts) to the landing pad. How far is the ring of fire from the ground? How far is the landing pad from where he starts?

Homework Equations

x=xo+vxo+at^2
y=yo+vyo+at^2

The Attempt at a Solution

I tried finding time and got 6/4 seconds but I don't know if it's correct or not.

 

[Thefox14]

Well this is a projectile motion problem, so we can say that the velocity in the x direction is constant and the velocity in the y direction is changing correct?

Knowing this, for part A how long does it take Zandor to go 60m in the x direction? Can you then relate this to how high up he is?

For part B, how long is Zandor in the air? Can you relate this to how far he traveled in the x direction?

 

[Ambidext]

Hmm- the first things you should find are the horizontal and vertical distances of the motion.

1. Split the initial velocity into vertical and horizontal components so you can calculate the height and the horizontal distance of the motion.

2. Calculate the time taken for the whole motion.

I got 5.13s for the motion's total time taken.


Edit: adding to what fox said,

you might consider the 60m as a ratio of the whole horizontal distance.

 

[runningirl]

i'm not i understand how to find the distances..
what equations am i supposed to use?

 

[Thefox14]

For part A)
There is no acceleration in the X direction correct? So the position formula for the x direction would be:
$$x_{f} = x_{0} + v_{x}t$$
We know what the final x position of the ring and his inital x position and velocity. So solve for the time it takes him to reach that x position, plug it into the position formula for the y direction and solve for y final

 

[runningirl]

is vx=40?

how am i supposed to figure out part B because i don't know the vy, do i?

 

[Thefox14]

No his TOTAL velocity is 40. The angle he's being shot at is 40 degrees though, so use some trig and break the velocity into the x and y components

 

[runningirl]

okay, i got part a to be 31.57 m and part b to be 100.67 m.
if anyone would like to check it i'd greatly appreciate it :)

 

[Thefox14]

Got the same for part A, but not for part B. I got 160.62m, looks like you subtracted the 60m from the starting point to the fire. Remember the question asks you the total distance to the landing pad from where he started.

 

[Ambidext]

The 4 equations I use for kinematics are:

s = v_it + 0.5at²
s = 0.5(v_i + v_f)t
v_f = v_i + at
v_f² = v_i² - 2as

Apply whichever equation that has the variables you are given, and as I said earlier, try to think of the distance as the ratio:

60m / s_total = t_60m / t_total

P.S. I use s for displacement.