5. Determine the total vertical distance the ball travels, in meters, during one throw. 13 Part...

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5. Determine the total vertical distance the ball travels, in meters, during one throw. 13 Part 2: Extending the model 6. On the planet Mars, the gravitational acceleration is -3.71 m/s. Determine the maximum height reached by a ball thrown vertically on Mars. Assume the same initial height and initial velocity that you used in Part 1. 13 7. On Jupiter, the gravitational acceleration is 2.5 times bigger than Earth's. Determine the time taken for the ball to hit the ground on Jupiter. Assume the same initial height and initial velocity that you used in Part 1. Now that you have a working quadratic function to model the height of the ball at any given time, use it to calculate the maximum height the ball reaches. 4. Graph the function h(t) by hand. (Use increments of 0.2 seconds on the t-axis, but you determine the best scale for the h(t)-axis). In addition, label the t-axis, h-axis, vertex, t-intercept and h-intercept. 13 13 Part 1: Analyzing the data 1. Your first goal is to determine the appropriate equation based on your data. Here the variables are t and h h is a function of t, i.e. h(t) The parameters (constants) are g, vo and ho (a) From the information provided, which parameter value(s) do you already know? State them. (b) Which parameter value(s) do you still need to solve for? Use the provided data to solve for your unknown parameter(s). Use appropriate function notation to show your work. Round your answers to the nearest tenth (1 decimal place). Write down the model equation you have obtained for h(t) with the appropriate values subbed in for the parameters. The equation is w that y ny given tir Quadratic Functions Assignment Learning Goal How High Can You Throw a Ball? I will understand how to create and apply a model of a quadratic equation. Success Criteria: I can create a quadratic equation to model real-life situations. I can solve for the roots of a quadratic equation. I can interpret the meaning of the roots of a quadratic equation. Introduction Application /20 The height, h(t) (in meters) as a function of time, t in seconds, of an object traveling vertically and being affected by force due to gravity can be modelled by the equation: 1 h(t) = 29t + vot + ho Where vo, ho and g are parameter (constants) Vo represents the initial velocity (in meters per second), ho represents the initial height (in meters) and g=-9.8 represents the gravitational acceleration on Earth (in meters per second) The Scenario A ball is thrown up and then it hits the ground. Two pieces of data are gathered from this situation: The height above the ground the ball was first thrown from The time it took for the ball to hit the ground after it was thrown Each student will be given slightly different data of this scenario. Use the #s below your name for assignment me Name: Yan Qun Shuo Sabrina Maria Yana Chloe Illiyaan Daniel Ola Gavin Height ball was thrown from (m) 1.2 1.3 1.4 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.2 Time for ball to hit 1.5 1.6 1.8 1.9 2.2 3.2 3.3 the ground (sec) 2.6 2.8 2.9 2.3 Name: Sebastian Height ball was = - - 1.2 1.3 1.4 thrown from (m) 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.2 Time for ball to hit the ground 2.2 1.9 1.7 1.6 16 (s) 1.5 1.4 2.8 3.3 2.6 2.3 2.9 5. Determine the total vertical distance the ball travels, in meters, during one throw. 13 Part 2: Extending the model 6. On the planet Mars, the gravitational acceleration is -3.71 m/s. Determine the maximum height reached by a ball thrown vertically on Mars. Assume the same initial height and initial velocity that you used in Part 1. 13 7. On Jupiter, the gravitational acceleration is 2.5 times bigger than Earth's. Determine the time taken for the ball to hit the ground on Jupiter. Assume the same initial height and initial velocity that you used in Part 1. Now that you have a working quadratic function to model the height of the ball at any given time, use it to calculate the maximum height the ball reaches. 4. Graph the function h(t) by hand. (Use increments of 0.2 seconds on the t-axis, but you determine the best scale for the h(t)-axis). In addition, label the t-axis, h-axis, vertex, t-intercept and h-intercept. 13 13 Part 1: Analyzing the data 1. Your first goal is to determine the appropriate equation based on your data. Here the variables are t and h h is a function of t, i.e. h(t) The parameters (constants) are g, vo and ho (a) From the information provided, which parameter value(s) do you already know? State them. (b) Which parameter value(s) do you still need to solve for? Use the provided data to solve for your unknown parameter(s). Use appropriate function notation to show your work. Round your answers to the nearest tenth (1 decimal place). Write down the model equation you have obtained for h(t) with the appropriate values subbed in for the parameters. The equation is w that y ny given tir Quadratic Functions Assignment Learning Goal How High Can You Throw a Ball? I will understand how to create and apply a model of a quadratic equation. Success Criteria: I can create a quadratic equation to model real-life situations. I can solve for the roots of a quadratic equation. I can interpret the meaning of the roots of a quadratic equation. Introduction Application /20 The height, h(t) (in meters) as a function of time, t in seconds, of an object traveling vertically and being affected by force due to gravity can be modelled by the equation: 1 h(t) = 29t + vot + ho Where vo, ho and g are parameter (constants) Vo represents the initial velocity (in meters per second), ho represents the initial height (in meters) and g=-9.8 represents the gravitational acceleration on Earth (in meters per second) The Scenario A ball is thrown up and then it hits the ground. Two pieces of data are gathered from this situation: The height above the ground the ball was first thrown from The time it took for the ball to hit the ground after it was thrown Each student will be given slightly different data of this scenario. Use the #s below your name for assignment me Name: Yan Qun Shuo Sabrina Maria Yana Chloe Illiyaan Daniel Ola Gavin Height ball was thrown from (m) 1.2 1.3 1.4 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.2 Time for ball to hit 1.5 1.6 1.8 1.9 2.2 3.2 3.3 the ground (sec) 2.6 2.8 2.9 2.3 Name: Sebastian Height ball was = - - 1.2 1.3 1.4 thrown from (m) 1.5 1.6 1.2 1.3 1.4 1.5 1.6 1.2 Time for ball to hit the ground 2.2 1.9 1.7 1.6 16 (s) 1.5 1.4 2.8 3.3 2.6 2.3 2.9