Physics homework help. Please help me!!!?

Question

Ok i have 3 questions from physics and i dont understand any of them. Could you please explain how to do it and give me the answer? I will give u best answer and my eternal gratitude!!! The questions are as follow:

1. A kid fires a slingshot pellet directly at a target that is far enough away to talk one-half-second to reach. How far below does the target hit? How high above should he aim? ( he is throwing a distance of 60meters standing on a platform 20meters high)...

2. The boy on the platform throws a ball a distance of 60 meters, as mentioned in number 1, at what speed is the ball thrown (in meters/second)?

3. A shiny new sports car sits in a parking lot of a car dealership. Above is a cargo plane flying horizontally at 50 m/s. At the exact moment the plane is 125 meters directly above the car, a heavy crate accidentaly falls from its cargo doors. Realative to the car, where will the crate hit? ( speed of gravity if needed can be rounded to 10m/s.)

Answer 1

Question 1, part 1, can be restated as to how far does an object fall in .5sec with gravity as the force and no air resistance.

The average velocity for the fall will be 1/2 *g * t
so the distance is 1/2* g * t^2
or 1/2 9.8 *1/4
or 9.8/8 meters
=1.225 meters

Question 1, part 2, requires that the intitial velocity of the pellet be calculated to determine the horizontal component with an azimuth added to hit the target.

60 meters in .5 secs is 120m/s velocity
With an azimuth, the horizontal component is
120 * cos theta = h velocity

with t as time to target
t*h=60m
so cos theta = 1/(2*t)

and the vertical component of velocity
v= 120 * sin theta

we also know that v=1/2 *g *t

The velocity components form a right triangle
so a^2 + b^2 = c^2
c=120
a= 60/t
b=1/2* g* t
rounding g to 10
25 t^4 -120^2 t^2 +60^2 = 0
t=.5001 s

this is close to .5, so the difference using .5 is negligible
it was fun doing the math, though

Note the multiple roots, I believe ther is only one real root that matters, though.

So he should aim 1.225 meters above the target and the pellet will be ever so slightly below the target.

I won't do the other two questions in this session.

j