assigment 5

1. Solve






2. Iffind

......


3. find the normal vector
field-a =

4. if a rocket is fired vertically upward from the earth's surface with initial velocity 192 ft / sec, when the rocket reaches its maximum height from the ground and what the maximum height? how long does it take to reach the ground again and how much speed when hitting the ground?

5. a weight W attached to a rope 50 feet long and through the point P, 20 feet above the ground. The other end of the rope attached to a truck at point A, 2 feet above ground level, if the truck was moving away at a speed of 9 ft / sec, how fast it loads up when he was 6 feet from the ground?

Answer:
1.

2.

3.




4. From that text, we get :
v = 192 – 32t
s = 192t – 16t^2
when v = 0
192 – 32t = 0
32t = 192
t = 6
So, the maximum height or altitude happen when t = 6
s = 192 (6) – 16(6) = 576 feet
That rocket reaches ground whe s = 0
192t - 16t^2 = 0
192t = 16t^2
t = 12
So, it needs 6 seconds to reaches ground again, t = 12
v = 192 – 32(12) = -192 feet/second
So, the last velocity equals initial velocity.

5. Suppose x is distance of improving load
Suppose y is a horizontal distance
From A , where that rope tiech with the truck , on vertical ine which through fulley