Martha passes a police officer at 30 m/s in a zone signed for a speed of 15m/s.

Question

Martha passes a police officer at 30 m/s in a zone signed for a speed of 15m/s. The officer starts in pursuit 1 second after martha passes with a constant acceleration of 3.0 m/s2. how long does it take the officer to catch Martha? How fast is he going when he catches her? a spring loaded gun shoots a .005 kg bullet verticaally upward with and initial velocity of 21 m/s. a) what is the height of the bullet 3 seconds after firing? b) at what time is the bullet 12m above the muzzle of the gun? and can you please tell me which formulas i would use for: you are driing along at 20 m/s on a road that heads at an angle of 25 degrees west of north. At what rate are you going a) north and b) west? Martha passes a police officer at 30 m/s in a zone signed for a speed of 15m/s. The officer starts in pursuit 1 second after martha passes with a constant acceleration of 3.0 m/s2. how long does it take the officer to catch Martha? How fast is he going when he catches her? a spring loaded gun shoots a .005 kg bullet verticaally upward with and initial velocity of 21 m/s. a) what is the height of the bullet 3 seconds after firing? b) at what time is the bullet 12m above the muzzle of the gun? and can you please tell me which formulas i would use for: you are driing along at 20 m/s on a road that heads at an angle of 25 degrees west of north. At what rate are you going a) north and b) west?

Explanation / Answer

1)
The speed of the plane 340 mi/h
The speed of the wind is 45 mi/h
The velocity of the plane with respect to the ground is sqrt(340^2+45^2) = 342.9 m/s
in the direction of south of east

2)
The acceleration a = 29.4 m/s
Time of travel t = 4 s
The velocity of the rocket at the end of 4 s, v = at
= 29.4*4
= 117.6 m/s
The distance travelled by the rocket in 4 s, H = vt
= 117.6*4
= 470.4 m
The rocket will travel with this velocity under the gravitation, and comes to rest at maximum height.
The further distance travelled by the rocket is h = v^2/2g
= 705.6 m
The total height of the rocket reached is h' = H+h                                                             h' = 1176 m From the maximum height the rocket falls under the gravity The final velocity v' = sqrt (2*g*h')                               = 151.8 m/s

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