d) Using a throwing stick, Dominic can throw his dog’s ball across the park. Assume that the park is flat. The path of the ball can be modelled by the equation y = −0.02x^2 + x + 1.8, where x is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres). (i) Find the y-intercept of the parabola y = −0.02x^2 + x + 1.8 (the point at which the ball leaves the throwing stick). (ii) (1) By substituting x = 20 into the equation of the parabola, find the coordinates of the point where the line x = 20 meets the parabola. (2) Using your answer to part (d)(ii)(1), explain whether the ball goes higher than a tree of height 8.5 m that stands 20 m from Dominic and lies in the path of the ball. (iii) (1) Find the x-intercepts of the parabola. Give your answers in decimal form, correct to two decimal places. (2) Assume that the ball lands on the ground. Use your answer from part (d)(iii)(1) to find the horizontal distance between where Dominic throws the ball, and where the ball first lands. (iv) Find the maximum height reached by the ball.
(d) Using a throwing stick, Dominic can throw his dog’s ball across the park. Assume that the park is flat. The path of the ball can be modelled by the equation
y = −0.02x^2 + x + 1.8,
where x is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres).
(i) Find the y-intercept of the parabola y = −0.02x^2 + x + 1.8 (the point at which the ball leaves the throwing stick).
(ii) (1) By substituting x = 20 into the equation of the parabola, find the coordinates of the point where the line x = 20 meets the parabola.
(2) Using your answer to part (d)(ii)(1), explain whether the ball goes higher than a tree of height 8.5 m that stands 20 m from Dominic and lies in the path of the ball.
(iii) (1) Find the x-intercepts of the parabola. Give your answers in decimal form, correct to two decimal places.
(2) Assume that the ball lands on the ground. Use your answer from part (d)(iii)(1) to find the horizontal distance between where Dominic throws the ball, and where the ball first lands.
(iv) Find the maximum height reached by the ball.
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