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A woman driving in a car on a level road manages to stay under a plane going up at a 30 degree angle. If the car is moving 1 10km/h, what is the speed of the plane? A boat is moving north at 8 km/h. A strong wind pushes the boat sideways to the left at 2 km/h AND the river current is pushing the boat 30 degrees south of east at 5 km/h. What is the boats final velocity (vector)? The brakes of a car can produce an acceleration of -6 m/sA2. (a) How long does it take to stop the car going 30 m/s? (b) How far does it travel during this time? A ball is thrown downward at 6 m/s. (a) how fast is it moving 2 sec later? (b) How far has it fall after the 2 sec?

Explanation / Answer

1) since the car is on a plane,

horizontal component of the plane = car's velocity

so plane's velocity * cos(30) = 110

or plane's velcoity = 110/cos(30)

= 127.07 km/hr

2) vertical component of the boat's velocity = 8- 5sin(30)

= 5.5 m/s

horizontal component of the velocity = 5cos(30)-2

=2.33

so boat's velocity vector = 5.5 i + 2.33 j

3)acceleration = -6

velocity = 30 m/s

let the distance covered be s.o,

v^2=u^2+2as

or 30^2-2*6*s=0

or s= 75 m

4) v=u+at

=6+9.81*2

= 25.62 m/s

b) distance covered = u*t+0.5a*t^2

=6*2 + 0.5*9.81*2*2

=31.62 m

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