4. A rocket entering Mars' atmosphere can accelerate at -20.0 m/s2. If the rocket is originally going 1600 m/s and has 10 seconds to reach its cruising velocity, what will that final velocity be?

v = 1400 m/s

Explanation:

Acceleration of the rocket, a = -20 m/s²

Initial speed of the rocket, u = 1600 m/s

Time, t = 10 s

We need to find the final velocity of the rocket. We can use first equation of motion to find it.

v = u+at

Put all the values,

v = 1600+(-20) (10)

= 1600-200

= 1400 m/s

So, the final velocity of the rocket is 1400 m/s.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west