Need help with 2 Kinematics questions (New to forum and physics)

Homework Statement:
1. Two aircraft depart simultaneously from the same location along perpendicular trajectories, with constant speeds equal to 300 km/h and 250 km/h, respectively. The two aircraft can communicate directly with each other only if they are less than 10 km apart. How long after departure will the two aircraft be out of communications range?

2. The New Horizons spacecraft was launched by NASA to study the dwarf planet Pluto in January of 2006. In July, 2015, the spaceship arrived at Pluto’s vicinity and sent back pictures of its surface. The estimated distance between Earth and the craft, at its closest approach point to Pluto, was 32 au (astronomical unit; 1 au = 1.50 × 108 km). Considering that the speed of light is 3.0 × 105 km/s, the image received by Earth observatories traveled, from New Horizons to Earth, during approximately:

A. 0.1μs
B. 1h
C. 4.5h
D. 2d
E. 0s
Relevant Equations:
⃗v = ∆⃗x ∆t
⃗x = ⃗x 0 + ⃗v t

⃗a = ∆⃗v ∆t
⃗v = ⃗v 0 + ⃗a t
v 2 = v 20 + 2 a ( x − x 0 )
⃗x = ⃗x + v⃗ t + 1 ⃗a t 2
I am new to physics and these are my last two questions of my homework. I am extremely confused on what to do but I do know that for question 1 I need to create a triangle and solve for the hypotenuse, and for question 2 I believe I need to input my given values into the equation for position/displacement: ⃗x = ⃗x + v⃗ t + 1 ⃗a t 2. However once again, I am extremely confused.

PeroK
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Homework Statement: 1. Two aircraft depart simultaneously from the same location along perpendicular trajectories, with constant speeds equal to 300 km/h and 250 km/h, respectively. The two aircraft can communicate directly with each other only if they are less than 10 km apart. How long after departure will the two aircraft be out of communications range?

2. The New Horizons spacecraft was launched by NASA to study the dwarf planet Pluto in January of 2006. In July, 2015, the spaceship arrived at Pluto’s vicinity and sent back pictures of its surface. The estimated distance between Earth and the craft, at its closest approach point to Pluto, was 32 au (astronomical unit; 1 au = 1.50 × 108 km). Considering that the speed of light is 3.0 × 105 km/s, the image received by Earth observatories traveled, from New Horizons to Earth, during approximately:

A. 0.1μs
B. 1h
C. 4.5h
D. 2d
E. 0s
Homework Equations: ⃗v = ∆⃗x ∆t
⃗x = ⃗x 0 + ⃗v t

⃗a = ∆⃗v ∆t
⃗v = ⃗v 0 + ⃗a t
v 2 = v 20 + 2 a ( x − x 0 )
⃗x = ⃗x + v⃗ t + 1 ⃗a t 2

I am new to physics and these are my last two questions of my homework. I am extremely confused on what to do but I do know that for question 1 I need to create a triangle and solve for the hypotenuse, and for question 2 I believe I need to input my given values into the equation for position/displacement: ⃗x = ⃗x + v⃗ t + 1 ⃗a t 2. However once again, I am extremely confused.

Let's see what you can do about the hypoteneuse in question 1. You don't seem so confused about that.

Hints for Problem #2:
It is given that the spacecraft traveled a distance of 32 au (the distance between Earth and its closest approach point to Pluto). The first thing we need to do is convert 32 au into kilometers, since the speed of light is given in units of km/s.
##32 \text{ au} = 1.50 \times 10^8 \text{ km}##
##(1.50 x 10^8)(32) = 4.80 \times 10^9 \text{ km}##

The question asks for the time it takes for light to travel from the spacecraft back to Earth at ##3.8 \times 10^5 \text{ km/s}##.
So, we already know that the distance is:
##Δx=4.80 \times 10^9 \text{ km}##
And it's given that:
##v=3.8 \times 10^5 \text{ km/s}##

So, all you need to do now is solve for t.

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Delta2