The problem I created was based on Hope Solo and her soccer skills. Hope kicks the ball back at an initial height of 3 feet, and a vertical velocity at 20 feet per second. The equation to this problem would be h(t)= -16t2 + 20t + 3. This shows how 20 would be the velocity, and 3 would be the initial height. The problem would ask us for the equation, time the ball would hit the ground in seconds, time the ball was in the air at 5ft, and the maximum height of the ball. In order to find at what time the ball would hit the floor, we need to find zero in the calculator. First step into solving this problem is plugging in the equation into the calculator.
You will the need to find zero under the x-axis, in trace zero. The calculator will ask you for left and right bound. The ball would then hit the ground at 1.4 seconds. Next, the problem asked for the time the ball hit 5 ft. The steps to make in the calculator is trace, value, and x=5 ft. The calculator would then find the time in seconds when the ball was 5 feet in the air. The ball was at 1.14 seconds when the ball hit 5 feet in the air. The problem also asked for maximum height. In order to find maximum height, you must go to trace, maximum, and the calculator would then ask you for left and right bound. If instructions are dont correctly, the maximum height would be 9.25 feet.
DeVon hits a baseball into the air with an initial vertical velocity of 60 feet per second and an initial height of 3 feet. Will Devons baseball clear a 60-foot brick wall 2 seconds after the ball was hit? In order to solve this problem, we must find the height the ball reaches at 2 seconds in the air. In order to do that, we must hit trace, value, and enter x=2. It then came to show that the ball reached 59 feet in 2 seconds. This proved that the ball will not pass 60 feet at 2 seconds. This makes sense because I know that the maximum height the ball reaches is 59.2 feet. 59.2 feet is lower than 60 feet. Therefore, the ball reaching 59 feet at 2 seconds does make sense. The ball was to go over the brick fence at 60 feet, but its highest peak is at 59.2. So, at no point in time will the ball reach over the 60 foot fence.
In conclusion, Math is all about using your prior knowledge, plugging it into what you know, to solve for what you dont know. The vertical motion model is made up of the velocity, and height. The equation is -16t2 + vt + h. V is equivalent to the velocity, and h is equal to the height. The vertical motion falls under the influence of gravity. As the force due to gravity may be opposite to the direction of motion, there exists the possibility that the body under force of gravity reverses its direction. It is, therefore, important to understand that the quantities involved in the equations of motion may evaluate to positive or negative values with the exception of time (t). We must appropriately assign sign to various inputs that goes into the equation and correctly interpret the result with reference to the assumed positive direction. Further, some of them evaluate to two values one for one direction and another of reversed direction. The vertical motion model is real life science and math. it works for any object that is effected by gravity.
G.R.A.S.P Goal; height at 2 seconds in the air
Required; h(t)= -16t2 + 60t + 3
Analyze; value; 2 seconds
X min; -10 Y-min; -50
X-max; 10 Y-max; 90
scl; 1 scl; 10
Solve; The ball will not reach 60 ft. at 2 seconds. It will reach 59 ft. at 2 seconds. Paraphrase; The ball will not reach 60 ft. at 2 seconds because the maximum height is 59.2. Therefore, if the balls highest point is 59.2, it can never reach 60 ft.