Question

The following function gives the height h meters, of a batted baseball as a function of the time, t seconds, since the ball was hit. 

h(t)=-4.5^2+13.5t+5.875 or https://i.gyazo.com/a83bb3b851c332dadc76e2462313605f.png 

A. What is the physical significance of the 5.875 for this situation? Prove this is true.

B. Determine the following characteristics: axis of symmetry, direction of opening, t and h intercepts, vertex, minimum/maximum.

Hint: Write in standard form.

C. Graph the model with all approapriate labels and restrictions. 

D. At what time does the ball hit the ground? 

E. What is the geometric significance of the left t-intercept of the graph? Why does this point have no real physical meaning?

Answer 1

Soln 6 h(t) = --4.5ť? +13.50 +5.875 the Sigts Physical significance of that inteel height of when it was hit. baseboll was S.B15m hlo -- 4.5 (0)2 + 13.5(0) +5.875 hlo) 5.075 m b ht) = -4.5+2+13.5t +17875 hrt) !! It +13:5 hill) toy maximum of minimum height t=1.5 see h't) -9 Ko so het) will maximum at t = 1.5 h (1-5) = -4.5 (15)2 + 13.5(1-5)+5.875 h115) 16 maximum height at lt=15*sed h (minimum) 0 at t = 3.3856 see

het) = -4.5+? + 13.50 +5.875" hit) = - - 4.5 [ +2-37 - 42 h(t) = -4.5 [(-3) -13] = -45(4-35) ? → Vertex (3116) axis symmetry hlt) - 16 4= 3/3 g hintercept t=0 hool 5.875 t intercept ho - 4,5t^+ 13++ C. 815 = 0 t = 3.3856,-0.3856 x No physical meaning t could not to as t. Increase h Increase [wire lo concane clown ward

© (1.5,16) maxima graph h(m) 5.875 11:5 7 385 t (see 2 axis og symmetr @ hit the ground t = 3.3656 see h = 0 e H Is lyt interpt of t=-0-3856 see not possible as it is always positive 14 has no physical significance.