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A flying cannonball’s height is described by formula y=−16t^2+300t. Find the highest point of its trajectory. In how many seconds after the shot will cannonball be at the highest point?

Respuesta :

Kalahira
Highest point = 1406.25 Number of seconds = 9.375 We've been given the quadratic equation y = -16t^2 + 300t which describes a parabola. Since a parabola is a symmetric curve, the highest value will have a t value midway between its roots. So using the quadratic formula with A = -16, B = 300, C = 0. We get the roots of t = 0, and t = 18.75. The midpoint will be (0 + 18.75)/2 = 9.375 So let's calculate the height at t = 9.375. y = -16t^2 + 300t y = -16(9.375)^2 + 300(9.375) y = -16(87.890625) + 300(9.375) y = -1406.25 + 2812.5 y = 1406.25 So the highest point will be 1406.25 after 9.375 seconds. Let's verify that. I'll use the value of (9.375 + e) for the time and substitute that into the height equation and see what I get.' y = -16t^2 + 300t y = -16(9.375 + e)^2 + 300(9.375 + e) y = -16(87.890625 + 18.75e + e^2) + 300(9.375 + e) y = -1406.25 - 300e - 16e^2 + 2812.5 + 300e y = 1406.25 - 16e^2 Notice that the only term with e is -16e^2. Any non-zero value for e will cause that term to be negative and reduce the total value of the equation. Therefore any time value other than 9.375 will result in a lower height of the cannon ball. So 9.375 is the correct time and 1406.25 is the correct height.

The number of seconds after the shot of cannonball will be at the highest point is; t = 9.375 seconds

We are given the height of a flying cannonball as a formula;

y = -16t² + 300t

      Now, the time at start and finish will occur at y = 0

Let us find the roots of the height equation to know the times at y = 0.

Thus, roots using online quadratic equation solver gives us;

t = 0 seconds and t = 18.75 seconds

This means total time of motion is 18.75 seconds

     Now, the maximum height will be achieved at half the time for the entire motion.

Thus, time at max height = 18.75/2 = 9.375 s

      Thus, highest point is gotten by putting 9.375 s for t in the height equation;

y_max = -16(9.375)² + 300(9.375)

y_max = -1406.25 + 2812.5

y_max = 1406.25 m

Read more at; https://brainly.com/question/2922810

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