The height of a football "t" seconds after a punt depends upon the intial height and velocity of the ball, and that on the downward pull of gravity. Supposed a punt leaves the kicker's foot at an initial height of .75 meters and with an initial velocity of 32 meters per second. what is a rule relating h(t) in meters and time t in seconds that the ball was in the air for this punt,.

Question

The height  of a football "t" seconds after a punt depends upon the intial height and velocity of the ball, and that on the downward pull of gravity. Supposed a punt leaves the kicker's foot at an initial height of .75 meters and with an initial velocity of 32 meters per second. what is a rule relating h(t) in meters and time t in seconds that the ball was in the air for this punt,.

anonymous · Answer

I will assume that initial velocity of 32 m/s is all in the vertical direction
then, the rule is:
h(t)=initial height+initial velocity*time+1/2 acceleration*time^2
acceleration due to gravity is 9.8 m/s^2
so
$$h(t)=.75+32t+1/2*9.8*t^2$$

anonymous · Answer

thank you very much