Select the correct answer.
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?
The equation for the height of an object in projectile motion can be modeled using the equation:
y = y0 + v0t + (1/2)gt^2
Where:
- y is the height at time t,
- y0 is the initial height,
- v0 is the initial velocity, and
- g is the acceleration due to gravity.
Based on this equation, the system of equations that models the projectile motion of the two balls are:
For Laura's ball:
y1 = 3 + 60t - 16t^2
For Kennedy's ball:
y2 = 2.5 + 55t - 16t^2
So, the correct system of equations that models the projectile motion of the two balls is:
y1 = 3 + 60t - 16t^2
y2 = 2.5 + 55t - 16t^2