Question

crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t, seconds?
$h(t)=-16t^{2}+v_{0}t + h_{0}$
$h(t)=-16t^{2}+v_{0}t + 14$
$h(t)=-16t^{2}+14t$
$h(t)=-16t^{2}+14t + 14$
done

Explanation:

Step1: Recall the motion formula

The general formula for vertical - motion is \(h(t)=-16t^{2}+v_{0}t + h_{0}\), where \(v_{0}\) is the initial velocity and \(h_{0}\) is the initial height.

Step2: Identify the values of \(v_{0}\) and \(h_{0}\)

Given that the vertical velocity \(v_{0}=14\) ft/s. When a cricket jumps, its initial height \(h_{0} = 0\) (assuming it starts from the ground level).

Step3: Substitute the values into the formula

Substitute \(v_{0}=14\) and \(h_{0}=0\) into \(h(t)=-16t^{2}+v_{0}t + h_{0}\). We get \(h(t)=-16t^{2}+14t+0=-16t^{2}+14t\).

Answer:

\(h(t)=-16t^{2}+14t\) (the second option)