Question

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laura and kennedy are at softball practice. laura hits a ball that is 3 feet above the ground with an initial upward velocity of 60 feet per second. kennedy
hits a ball that is 2.5 feet above the ground with an initial upward velocity of 55 feet per second
if x is the time, y is the height of the ball, and the acceleration due to gravity is -32 feet per square second, which system of equations models the projectile
motion of the two balls?
a. ( y=-16 x^{2}+60 x + 3 )
( y=-16 x^{2}+55 x + 2.5 )
b. ( y=-3 x^{2}+60 x + 16 )
( y=-2.5 x^{2}+55 x + 16 )
c. ( y=-16 x^{2}+60 x + 2.5 )
( y=-16 x^{2}+55 x + 3 )
d. ( y=-16 x^{2}+60 x )
( y=-16 x^{2}+55 x )

Explanation:

Step1: Recall the projectile motion formula

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

Step2: Find the equation for Laura's ball

For Laura, \(v_{0}=60\) (initial velocity) and \(h_{0} = 3\) (initial height). Substituting into the formula gives \(y=-16x^{2}+60x + 3\).

Step3: Find the equation for Kennedy's ball

For Kennedy, \(v_{0}=55\) (initial velocity) and \(h_{0}=2.5\) (initial height). Substituting into the formula gives \(y=-16x^{2}+55x + 2.5\).

Answer:

A. \(y=-16x^{2}+60x + 3\), \(y=-16x^{2}+55x + 2.5\)