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=−16t2+30t+2 , which of the following correctly identifies the y-intercept and best explains its meaning?(1 point) Responses The y-intercept is at (0,2) . The shirt will reach the ground after 2 seconds from being launched. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirt will reach the ground after 2 seconds from being launched. The y-intercept is at (0,0) . The shirts are launched from the ground. The y -intercept is at left parenthesis 0 comma 0 right parenthesis . The shirts are launched from the ground. The y-intercept is at (2,0) . The shirts are launched at an initial height of 2 feet. The y -intercept is at left parenthesis 2 comma 0 right parenthesis . The shirts are launched at an initial height of 2 feet. The y-intercept is at (0,2) . The shirts are launched at an initial height of 2 feet. The y -intercept is at left parenthesis 0 comma 2 right parenthesis . The shirts are launched at an initial height of 2 feet.
1 answer
The correct answer is: The y-intercept is at (0, 2). The shirts are launched at an initial height of 2 feet.
In the given function \( y = -16t^2 + 30t + 2 \), the y-intercept occurs when \( t = 0 \). Plugging 0 in for \( t \) gives \( y = 2 \). This indicates that at the moment the T-shirts are launched (when time \( t \) is 0), they are 2 feet above the ground, which reflects the height of the golf cart from which they are launched.
