Solutions
KM#2: Sunset Crater (Level 2)
Mathematical Content: Basic algebra; solving equations
SOLUTIONS: KM # 2 Sunset Crater
Question 1: What is the initial velocity? To answer this, follow the steps below. Use meters for height and distance.
A) What is the height and the distance when the volcanic bombs hit the ground? (These are the values of z and u when t = tmax)
The height is z = 0 and the distance is u = 800 meters.
B) Re-write formula 1 for z by substituting
and.
.
C) Use formula 2 and your answer to step A to write an equation for tmax in terms of v0.
D) Substitute your answers from steps A, B, and C in the equation for z when 
and solve for 
. Solve:
Question 2: What is tmax? (Use formula 2.)
Question 3: What is V, the total velocity at impact? (Use formula 3.)
: 
Question 4: Repeat the above steps to Question 1 with u = 2000 m.
A) What is the height and the distance when the volcanic bombs hits Steve’s house? (These are the values of z and u when t = tmax)
The height is z = 0 and the distance is u = 2000 meters.
B) As before, formula 1 is 
C) Use formula 2 and your answer to step A to write an equation for tmax in terms of v0.
D) Substitute your answers from steps A, B, and C in the equation for z when 
and solve for 
.
Solve
It requires an initial velocity of v0 = 130.6 m/s to destroy Steve’s home.