Question

Sara jumps off a diving board that is 6 feet above the surface of the water her height above the surface of the water h in feet is a function of time t in seconds as modeled by the quadratic function h(t)=-2t^2 + t + 6 how many seconds did it take sara to hit the surface of the water after she jumped off the diving board

Answer 1

Well when she hits the water h=0 so

2t^2-t-6=0 factor

2t^2-4t+3t-6=0

2t(t-2)+3(t-2)=0

(2t+3)(t-2)=0, since t>0

t=2 seconds...

However it should be noted that h(t)=-2t^2+t+6 implies that

v(t)=dh/dt=-4t+1 and

a(t)=dv/dt=-4

Since this is a free fall equation, this would suggest that the acceleration due to gravity is -4, whether that is supposed to be -4ft/s^2 or -4m/s^2, it certainly is not on this planet! :D If it is -4ft/s^2 it could be on the Moon or if it is -4m/s^2 it could be on Mars.