Fill in the blanks in the questions below.

A rock is fired from a slingshot on a hill 48 feet over a field at an initial vertical speed of 32 feet per second. The rock will go up and then fall down to the field. The height of the rock is given by the equation h = -16t2 + 32t + 48, where t is time in seconds. The maximum height of the rock is _ feet. It is reached after _ seconds.

Question

09-06-2022
Mathematics

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Fill in the blanks in the questions below.

A rock is fired from a slingshot on a hill 48 feet over a field at an initial vertical speed of 32 feet per second. The rock will go up and then fall down to the field. The height of the rock is given by the equation h = -16t2 + 32t + 48, where t is time in seconds. The maximum height of the rock is _ feet. It is reached after _ seconds.

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xero099 xero099 · Answer 1 · 2022-06-20T18:06:36+02:00

After studying the graph and locating the vertex of the parabola. The maximum height of the rock is 64 feet. It is reached after a second.

How to obtain information from free fall equation by graphical approach

Free fall is an uniformly accelerated motion due to gravitation, whose expression is of the form:

h = -(1/2) · g · t² + v' · t + h' (1)

Where:

g - Gravitational constant, in feet per square second.
v' - Initial speed, in feet per second.
h' - Initial height, in feet
t - Time, in seconds

Graphically speaking, the model represents a parabola. The maximum height is the vertical component of the vertex of the curve and its time is the horizontal component.

Hence, the maximum height of the rock is 64 feet. It is reached after a second.

To learn more on parabolas: https://brainly.com/question/4074088

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