Question

The chitauritwo is flying past Hawkeye who is stationed on top of a building. The trajectory of the chitauritwo is given by the equations
xc = -100m + tm/s + ½(0.1)t^2
yc = 100m
zc = 440m
Hawkeye’s position is given by xc = 0, yc = 0, and zc = 440m.
if he is to fire an arrow with an initial velocity of 137m/s at time t=0, will he be able to shoot the chitauritwo? In what direction should he fire his arrow? Ignore air resistance, because the arrow is so fast, and note that the gravity acts in the negative z-direction.

The unknown variables in this problem seem to be the speed of the river, the speed of the canoe relative
to the river and the time it takes from when they turn around to when they retrieve the bottle. 3
unknowns.
i. Write down an equation in terms of the 3 unknowns for the students canoeing upstream. This is of the
form, velocity is equal to distance over time.
ii. Write down a similar equation in terms of the 3 unknowns for the students canoeing down stream to
retrieve the bottle.
iii. Write down a similar equation in terms of the 3 unknowns for the journey of the bottle from when it
was first dropped to when it was retrieved.
iv. You now have 3 equations and 3 unknowns. Do the algebra and solve the problem.

Please help me with this, really stuck :l
Thanks a lot :)

Answer 1

Please Help :(

Answer 2

@ybarrap @kc_kennylau @atlas

Answer 3

Thanks @sarah786 hope i get some help

Answer 4

The questions at the end about "students canoeing" seem to have nothing to do with Chitauritwo and Hawkey in the 1st part of the problem.

For the 1st part of the problem, is this how you see this setup?


Chitauritwo'c Coordinates:
$$
\large{
x_c = -100 + t + \cfrac{1}{2}0.1t^2\\
y_c=100\\
z_c=440
}
$$
Hawkeye's Coordinates:
$$
x_c=0\\
y_c=0\\
z_c=440
$$

Now, Hawkeye shoots his arrow in a certain direction to hit Chitauritwo. Direction is really his only variable because speed of the arrow was give as 137 m/s.

We want to know if he will be able to shoot the Chitauritwo.

We will need the SUVAT equations - http://en.wikipedia.org/wiki/SUVAT_equations#Constant_linear_acceleration