Attempt following question by selecting a choice to answer.
c
The height S feet reached in time
t seconds by a stone projected vertically upwards is given by
S = 192t - 16t2. What is the maximum height reached by the stone?
cc ccA.
c32 ft
B.
c 576 ft
C.
c6 ft
D.
c1152 ft
c
B
Step 1: The height reached by the stone in time t is S = 192t - 16t2
Step 2: The velocity of the stone at time t = V = dSdt[Definition.]
Step 3: = ddt (192t - 16t2)[Substitute S from step 1.]
Step 4: ÞV = 192 - 32t
Step 5: At the maximum height, V = 0
Step 6: 192 - 32t = 0 ® t = 19232= 6 sec.[Solve for t.]
Step 7: After the projection, the stone reaches the maximum height in 6 sec.
Step 8: So, the maximum height reached by the stone = 192(6) - 16(6 )2
Step 9: = 1152 - 576
Step 10: = 576 ft.