A football is kicked into the air. It's height in meters after t seconds is given by h= -4.9(t-2.4)^2+29

Question

a. What was the height of the football when it was kicked?

b. What was the maximum height of the ball? At what time was the maximum height reached?

c. How high was the ball after 2 seconds?

d. Was the ball still in the air after 5 seconds?

Answer 1

a. substitute 0 for t (time of 0 is when it was kicked) 

h = -4.9(-2.4)²+29 = 0.776 m

 

b. the max height is the vertex of the parabola (note, the vertex is 2.4 s to the right and 29 m up from the origin) - the max height will occur at t = 2.4 s, or 29 m

 

c. substitute 2 s for t, so h = -4.9(2-2.4)² + 29 = 28.87 m

 

d. substitute 5 s for t, so h = -4.9(5-2.4)² + 29 = -4.124 m ---> a negative value here implies that the ball reached the ground (and then continued for a "negative" height) - since it stops at the ground or h = 0, it is no longer in the air after 5 seconds