# Homework Practice Help

#### shivam28

Hello all,

I am nearly done my Kinematics homework and just need help with two more questions which I have tried countless times to complete on my own. Any help would be very appreciated. Please be aware I am a student taking Physics for the first time. These are the following questions:

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

Thank you very much!

#### topsquark

Forum Staff
Hello all,

I am nearly done my Kinematics homework and just need help with two more questions which I have tried countless times to complete on my own. Any help would be very appreciated. Please be aware I am a student taking Physics for the first time. These are the following questions:

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

Thank you very much!
Please let us know what you've been able to do with this so far. We can only help you if we know where you're stuck.

-Dan

#### Woody

For 1,
The paths of the two planes form a right angled triangle with the line of communication between them being the hypotenuse.
It should be reasonably easy to work out 2 equations giving the distance of each of the two planes from their starting point against time (since each is travelling at a constant speed).
You then have two equations giving the length of the two sides of a right angled triangle (with respect to time)

The length of the hypotenuse (the communication distance) is then the square-root of the sum of the squares of these two equations (against time)
Find out what value of time makes this distance 10km.

2 is pretty trivial, I am surprised that you are having difficulty.
are you just confused by the Big numbers
are you familiar with the notation used when dealing with these huge numbers?