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<p>The height, <code class='latex inline'>h</code>, of a football in metres <code class='latex inline'>t</code> seconds since it was kicked can be modelled by <code class='latex inline'>\displaystyle h = -4.9t^2 + 22.54t + 1.1 </code></p><p>a) What was the height of the football when the punter kicked it?</p><p>b) Determine the maximum height of the football, correct to one decimal place, and the time when it reached this maximum height.</p>
Similar Question 2
<p>The path of a football can be modelled by the equation <code class='latex inline'>h = -0.0625d(d - 56)</code>, where <code class='latex inline'>h</code> represents the height, in metres, of the football above the ground and <code class='latex inline'>d</code> represents the horizontal distance, in metres, of the football from the player.</p><p>a) At what horizontal distance does the football land?</p><p>b) At what horizontal distance does the football reach its maximum height? What is its maximum height?</p>
Similar Question 3
<p>The path of a football can be modelled by the equation <code class='latex inline'>h = -0.0625d(d - 56)</code>, where <code class='latex inline'>h</code> represents the height, in metres, of the football above the ground and <code class='latex inline'>d</code> represents the horizontal distance, in metres, of the football from the player.</p><p>a) At what horizontal distance does the football land?</p><p>b) At what horizontal distance does the football reach its maximum height? What is its maximum height?</p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
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<p>The path of a football can be modelled by the equation <code class='latex inline'>h = -0.0625d(d - 56)</code>, where <code class='latex inline'>h</code> represents the height, in metres, of the football above the ground and <code class='latex inline'>d</code> represents the horizontal distance, in metres, of the football from the player.</p><p>a) At what horizontal distance does the football land?</p><p>b) At what horizontal distance does the football reach its maximum height? What is its maximum height?</p>
<p>The height, <code class='latex inline'>h</code>, of a football in metres <code class='latex inline'>t</code> seconds since it was kicked can be modelled by <code class='latex inline'>\displaystyle h = -4.9t^2 + 22.54t + 1.1 </code></p><p>a) What was the height of the football when the punter kicked it?</p><p>b) Determine the maximum height of the football, correct to one decimal place, and the time when it reached this maximum height.</p>
<p>A ball is thrown upward at an initial velocity of <code class='latex inline'>15</code> m/s, from a height of <code class='latex inline'>1.5</code> m. The height, <code class='latex inline'>h</code>, in metres, of the ball above the ground after t seconds can be found using the relation <code class='latex inline'>h = -4.9t^2 + 15t + 1.5</code></p><p>(a) Graph this relation using a graphing calculator.</p><p>(b) Describe the relationship between time and height.</p>
<p>The height of a ball thrown from the top of a ladder can be approximated by the formula <code class='latex inline'>h=-2t^2+4t+48</code>, where <code class='latex inline'>t</code> is the time, in seconds, and <code class='latex inline'>h</code> is the height, in metres.</p><p>a) Write the formula in factored form.</p><p>b) Determine when the ball will hit the ground.</p>
<p>Deanna throws a rock from the top of a cliff into the air. The height of the rock above the base of the cliff is modeled by the equation <code class='latex inline'>h = -5t^2 + 10t + 75</code>, where <code class='latex inline'>h</code> is the height of the rock in metres and <code class='latex inline'>t</code> is the time in seconds.</p><p>a) How high is the cliff?</p><p>b) When does the rock reach its maximum height?</p><p>c) What is the rock&#39;s maximum height?</p>
<p>A parachutist jumps from a plane 3500 m above the ground. The height, <code class='latex inline'>h</code>, in metres, of the parachutist above the ground t seconds after the jump can be modelled by the function <code class='latex inline'>h(t) = 3500 -4.9t^2</code></p><p>a) What type of function is h(t)?</p><p>b) Without calculating the finite differences, determine</p> <ul> <li>i) which finite differences are constant for this polynomial function</li> <li>ii) he value of the constant finite differences</li> </ul> <p>c) Describe the end behaviour of this function assuming there are no restrictions on the domain.</p><p>d) Graph the function. State any reasonable restrictions on the domain.</p><p>e) What do the <code class='latex inline'>t</code>—intercepts of the graph represent for this situation?</p>
<p>The height of a super ball, <code class='latex inline'>h</code>, in metres, can be modelled by <code class='latex inline'>h=-4.9t^2+10.78t+1.071</code>, where <code class='latex inline'>t</code> is the time in seconds since the ball was thrown.</p><p><em>a)</em> How many zeros do you expect this relation to have? Why?</p><p><em>b)</em> Verify your answer for part a) algebraically.</p>
<p>The path of a rocket fired at a Canada Day fireworks display is given by <code class='latex inline'>h = -4.9t^2 + 19.6t + 0.4</code>, where h is the height, in metres, of the rocket above the ground and t is the time, in seconds.</p><p>(a) Make a table of values for t = 0 to t = 4.</p><p>(b) Make a table of first and second differences. What conclusion can you make?</p><p>(c) Draw a graph of the path of the rocket using the table of values from part a) or graphing technology. Describe the path of the rocket.</p><p>(d ) How high above the ground was the rocket when it was set off? Explain your answer.</p>
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