A cannonball is shot upward from the upper deck of a fort with an initial velocity of 192 feet per second. The deck is 32 feet above the ground.
Use this formula to solve the problem: h = -16t2+v0t+h0
Quadratic Model: -16t2+192t+32
I solved this problem using mostly my graphing calculator. I typed in the function into "y =". Then I found the maximum point in the line using "2ND TRACE". This value is the answer for how high the cannonball went. I found how long the cannon ball was in the air by looking at the table and seeing when the line gets to 32 a second time because the first was when the cannonball was fired so the second is when it lands. The x value is the same as the t or time.
Math Component/ Formula and Expected Results: We used the range formula of R= (Vo2sin 2q)/g. R is the range of the nerf ball, the V is the initial velocity (estimated), q is the launch angle, and g is gravity which is always 32.2 meters per seconds squared. We estimated our initial velocity to be 10 meters per second and multiplied it by sin 2(45) and divided that by 32.3. The answer came out to be about 3.1 meters but after we converted to feet it was 10.2 feet.
Use this formula to solve the problem: h = -16t2+v0t+h0
Quadratic Model: -16t2+192t+32
1. How high does the cannonball go? ___608 feet___ (Remember you are looking for a specific part of the vertex.)
2. How long is the cannonball in the air? __12 seconds_ (Remember you can use the quadratic formula.)
I solved this problem using mostly my graphing calculator. I typed in the function into "y =". Then I found the maximum point in the line using "2ND TRACE". This value is the answer for how high the cannonball went. I found how long the cannon ball was in the air by looking at the table and seeing when the line gets to 32 a second time because the first was when the cannonball was fired so the second is when it lands. The x value is the same as the t or time.
Math Component/ Formula and Expected Results: We used the range formula of R= (Vo2sin 2q)/g. R is the range of the nerf ball, the V is the initial velocity (estimated), q is the launch angle, and g is gravity which is always 32.2 meters per seconds squared. We estimated our initial velocity to be 10 meters per second and multiplied it by sin 2(45) and divided that by 32.3. The answer came out to be about 3.1 meters but after we converted to feet it was 10.2 feet.
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