An orange is shot up into the air with a catapult. The function h given by h(t)=15+60t−16t2 models the orange's height, in feet, t seconds after it was launched. Select all the true statements about the situation.

Question

An orange is shot up into the air with a catapult. The function h  given by h(t)=15+60t−16t2  models the orange's height, in feet, t  seconds after it was launched.     Select all the true statements about the situation.

Bytelearn · Accepted Answer

Identify Function Components:  Identify the function and its components. The function given is h(t) = 15 + 60t - 16t^2. This is a quadratic equation where: - 15 is the initial height (in feet) from which the orange is launched. - 60t represents the initial velocity impact on height per second. - -16t^2 represents the acceleration due to gravity impacting the height.Determine Initial Height:  Determine the initial height of the orange at t = 0 seconds. Substitute t = 0 into the function: h(0) = 15 + 60(0) - 16(0)^2 = 15 feet. This means the orange starts 15 feet above the ground.Calculate Vertex for Maximum Height:  Calculate the vertex of the parabola to find the maximum height and the time it occurs. The vertex formula for a parabola given by ax^2 + bx + c is t = -b/(2a). Here, a = -16 and b = 60. t = -60/(2*(-16)) = -60/(-32) = 1.875 seconds. Substitute t = 1.875 back into the height function to find the maximum height: h(1.875) = 15 + 60(1.875) - 16(1.875)^2 = 15 + 112.5 - 56.25 = 71.25 feet.

An orange is shot up into the air with a catapult. The function $h$ given by $h(t)=15+60t-16t^2$ models the orange's height, in feet, $t$ seconds after it was launched. Select all the true statements about the situation.

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An orange is shot up into the air with a catapult. The function hhh given by h(t)=15+60t−16t2h(t)=15+60t-16t^2h(t)=15+60t−16t2 models the orange's height, in feet, ttt seconds after it was launched. Select all the true statements about the situation.

An orange is shot up into the air with a catapult. The function $h$ given by $h(t)=15+60t-16t^2$ models the orange's height, in feet, $t$ seconds after it was launched. Select all the true statements about the situation.