degreeplus
New member
- Joined
- Oct 7, 2006
- Messages
- 24
This is a series of problems:
Use a(t) = -32 ft/sec^2 as the acceleration due to gravity. (Neglect air resistance.)
1) Show that the height above the ground of an object thrown upward from a point s feet above the ground with an initial velocity of v feet per second is geven by the function f(t) = -16t^2 + v(t) + s
My solution:
. . .a(t) = f''(t) = -32
. . .v(t) = f'(t) = -32t + c1
. . .f(t) = -32(1/2)t^2 + c1(t) + c2
. . .d(t) = f(t) = -16t^2 + v(t) + s
...where c1 = v and c2 = s
Here is where I have trouble:
2) With what initial velocity must an object be thrown upward (from ground level) to reacha maximum height of 550 feet?
This is how I thought about it:
. . .550/(t^2) = -32
...because acceleration is in units of distance/time^2. So then I kind of forced t = 4.146 sec (approximate), but it should be imaginary number instead.
. . .-16(4.146)^2 + v(4.146)
Then I get:
. . .550 = -275 + v(4.146)
. . .v = 198.988 (approximate)
But the book says "v = 187.617". I have tried other ways of solving but this is the closest I got to getting the correct answer numerically.
Help would be appreciated. I can't think of another way to solve this.
Use a(t) = -32 ft/sec^2 as the acceleration due to gravity. (Neglect air resistance.)
1) Show that the height above the ground of an object thrown upward from a point s feet above the ground with an initial velocity of v feet per second is geven by the function f(t) = -16t^2 + v(t) + s
My solution:
. . .a(t) = f''(t) = -32
. . .v(t) = f'(t) = -32t + c1
. . .f(t) = -32(1/2)t^2 + c1(t) + c2
. . .d(t) = f(t) = -16t^2 + v(t) + s
...where c1 = v and c2 = s
Here is where I have trouble:
2) With what initial velocity must an object be thrown upward (from ground level) to reacha maximum height of 550 feet?
This is how I thought about it:
. . .550/(t^2) = -32
...because acceleration is in units of distance/time^2. So then I kind of forced t = 4.146 sec (approximate), but it should be imaginary number instead.
. . .-16(4.146)^2 + v(4.146)
Then I get:
. . .550 = -275 + v(4.146)
. . .v = 198.988 (approximate)
But the book says "v = 187.617". I have tried other ways of solving but this is the closest I got to getting the correct answer numerically.
Help would be appreciated. I can't think of another way to solve this.
