How do you solve a and b?

Question

A stone is thrown straight up from the edge of a roof, 650 feet above the ground, at a speed of 12 feet per second.

 

A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 4 seconds later? 


B. At what time does the stone hit the ground?  6.76


C. What is the velocity of the stone when it hits the ground?

Answer 1

h(t) = (-1/2)gt² + v₀t + h₀

 

h(t) = -16t² + 12t + 650

 

(A)

 

h(4) = ?

 

Just plug t = 4 into the expression for h(t).

 

(B)

 

Set h(t) = 0 and solve for t.  You should get a positive and a negative solution for t when you apply the quadratic formula.  Discard the negative solution, since time starts at t = 0.

 

(C)

 

Integration of 

 

a = -g

 

with initial conditions gives

 

v(t) = 12 - gt = 12 - 32t  [v in ft/s]

 

Evaluate v(t) at the time computed in part (B). It should come out negative, indicating downward motion.