Height and Distance If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0. Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can see, the height is greater than the distance travelled. However, this is not always the case. The height may be less than or equal to the distance; this depends on the equation. ▶Determine what the values of parameters a and b have to be for the height of the trajectory to be greater than the distance travelled. Explain your reasoning by justifying each step in your calculations.
Height and Distance If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0. Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can see, the height is greater than the distance travelled. However, this is not always the case. The height may be less than or equal to the distance; this depends on the equation. ▶Determine what the values of parameters a and b have to be for the height of the trajectory to be greater than the distance travelled. Explain your reasoning by justifying each step in your calculations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Height and Distance
If an object is projected from the ground and lands on the ground some distance away, it follows a parabolic
trajectory that may be graphed in the first quadrant of a Cartesian plane. When the trajectory is represented
in this way, its equation may be written in the following form: y = ax² + bx, where a <0 and b>0.
Consider the height h of the object's trajectory and the distance d it travels. In the graph above, as you can
see, the height is greater than the distance travelled. However, this is not always the case. The height may
be less than or equal to the distance; this depends on the equation.
Determine what the values of parameters a and b have to be for the height of the trajectory
to be greater than the distance travelled. Explain your reasoning by justifying each step in
your calculations.
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