How to Calculate Javelin Throw Dynamics in Projectile Motion?

[kpadgett]

Homework Statement

Jill throws a Javelin by first accelerating it from rest through 85 cm and releasing it from a height
of 2.2 m at an angle of 35 degrees and it goes a distance of 62 m.

A) What are the values of the vertical and horizontal components of initial velocity?

B) Find the following:
X-initial position, Y-initial position
X-final pos., Y-final pos.
X-velocity initial, X-velocity final
Y-velocity initial, X-velocity final
Acceleration in x and y direction
and t-final for X and Y

C) What is the magnitude of the impact velocity vector?

D) What is the impact angle?

Homework Equations

I'm sure I have missed one:
V=(ds/dt)
a= (Vf-Vi)/(tf-ti)
x(t)=xi + (Vx)(t)
y(t)=yi + (Vy)(t) - (1/2)gt^2)

The Attempt at a Solution

I started writing down all my known terms and have the following from the given info:
Xi = 0
Yi = 2.2m
ax = 0
ay = -g = 9.8m/s^2
Yf = 0
Xf + 62
Theta = 35 degrees

At this point I went to plug known values into the x(t) and y(t) equations to find unknowns. The needed unknowns I see now are velocity and time of impact.

I am completely stumped on the next step to take from here to find velocity or time of impact. Any help would be appreciated.

 

[gneill]

So, does the "initial" position and velocity of the javelin correspond to when it was released by Jill, or to its position when it first begins to accelerate? The problem statement is not specific about this so it's badly posed by its author. Just thought I'd mention that.

Assuming that the author meant the initial position and velocity correspond to the instant of release then you need to write the kinematic equations for the horizontal and vertical motions that take place from that instant until the javelin lands. Set the initial x position to zero and the initial height to the given release height for that instant. The initial velocity should be decomposed into components via the appropriate trigonometry. The javelin "lands" when its vertical height reaches zero. Two equations in two unknowns: Solve for v and time to impact.

 

[kpadgett]

I have been sitting here trying to find which variable to choose, and which equation to try to work with the find t or v. There just seems to be an unknown variable too many in every one. I also wonder about the wording. I just need a hint to get started on this.

 

[haruspex]

You need to introduce an unknown for the launch velocity, v. Since you know the launch angle, you can write the horizontal and vertical launch speeds in terms of that. So for the price of one unknown you get two initial variables.
You can do the same with time. The time taken is the same for both horizontal and vertical motions. So your two 'distance = initial distance + initial speed * time + etc.' equations share two unknowns - solve.

 

[Nickie]

I would suggest approaching this problem by breaking it down into smaller parts and using the equations you have listed to solve for the unknowns.

For part A, you can use the initial velocity equation v = u + at to solve for the horizontal and vertical components of the initial velocity. The initial velocity will be the same in both directions, so you can set up two equations using the given information and solve for the unknowns.

For part B, you can use the equations for position and velocity in the x and y directions to solve for the unknowns. You have already correctly identified the known and unknown values for these equations, so you can plug them in and solve for the unknowns.

For part C, you can use the equation for magnitude of a vector, which is given by the square root of the sum of the squares of its components. In this case, the impact velocity vector will have both a horizontal and vertical component, which you can find using the equations from part A.

For part D, you can use the inverse tangent function to find the angle of the impact velocity vector, using the horizontal and vertical components found in part A.

Overall, it is important to carefully organize and label your known and unknown values and use the appropriate equations to solve for them. I hope this helps!