Question

Can someone help me solve this problem? http://i158.photobucket.com/albums/t120/brinazarski2/q_zpsaa3f3b75.png

Answer 1

I'm especially confused by what it means by the interval...

Answer 2

it means it turns a random angle between 0 and pi radians

Answer 3

so angle alpha is between 0 and 180 degrees?

Answer 4

yes, same thing, just different units

Answer 5

So it's basically this?

Answer 6

not quite. It's going in a straight line and either continues going in a straight line (that would be 0 degrees) or turns around backwards (that would be 180 degrees)

Answer 7

clearly if it keeps going straight the total distance is more than 7. If it turns around the total distance is less than 7. Find the critical angle at which the distance AC is exactly 7.

Answer 8

then you'll know the proportion of the possible angles at which the distance travelled is less than 7 and that 'll be your answer

Answer 9

I'm still confused..

Answer 10

in the first case with angle = 0, the total distance travelled is 13.
when angle=180 total distance is 3.
when angle=9 total distance is sqrt(8^2+5^2)

Answer 11

as the turn gets steeper and steeper the total distance from A to C gets smaller and smaller, from a maximum of 13 to to minimum of 3. your job is to find where it reaches 7.

Answer 12

If it were 180, wouldn't it be the same as 0?

Answer 13

no, 0 means it doesn't turn, 180 means it turns around and goes backwards.

Answer 14

Actually, I have to find the probability that it equals seven... so how would i find that probability?

Answer 15

take look at diagram; you now know length of all 3 sides of the triangle;
just use law of cosines to find the angle at which the object changed direction.
now the probability of the angles being chosen out of the uniform interval from 0 to pi is just the angle (in radians)/(pi - 0) = angle/pi, i think you should find it's the 4th answer choice :)