Question

the cheerleaders at a football game launch t - shirts into the crowd from the back of a golf cart that is 2 feet off the ground. the t - shirts have an upward velocity of 30 feet per second. using the function ( y=-16 t^{2}+30 t + 2 ), which of the following correctly identifies the y - intercept and best explains its meaning? (1 point)
o the y - intercept is at ( (0,0) ). the shirts are launched from the ground.
o the y - intercept is ( (0,2) ). the shirts are launched at an initial height of 2 feet.
o the y - intercept is at ( (0,2) ). the shirt will reach the ground after 2 seconds of being launched.
o the y - intercept is at ( (2,0) ). the shirts are launched at an initial height of 2 feet.

Explanation:

Step1: Recall the formula for projectile motion

The general formula for the height \(y\) of an object in projectile motion is \(y = - 16t^{2}+v_{0}t + y_{0}\), where \(v_{0}\) is the initial velocity and \(y_{0}\) is the initial height.

Step2: Identify the \(y -\)intercept

For the function \(y=-16t^{2}+30t + 2\), when \(t = 0\) (the initial time), we substitute \(t = 0\) into the function: \(y=-16(0)^{2}+30(0)+2=2\). So the \(y -\)intercept is at the point \((0,2)\). This means the initial height of the object (in this case, the T - shirt) is 2 feet.

Answer:

The \(y -\)intercept is at \((0,2)\). The shirts are launched at an initial height of 2 feet.