A bullet is shot straight upward with an initial speed of 925 ft/s. The height of the bullet after t seconds is modeled by the function h(t) = −16t2 + 925t where h is measured in feet. Use the function h to find the average speed of the bullet during the given time intervals.
Answers
462.5 ft /sec the average speed of the bullet during total flight
Step-by-step explanation:
Time interval is not given to find answer
h(t) = −16t² + 925t
dh/dt = -32t + 925
=> t = 925/32
d²h/dt² = - 32
Maximum height at t = 925/32
Max height = -16(925/32)² + 925(925/32)
= - 925² / 32 * 2 + 925² / 32
= 925² / 64
Average Speed = Total Distance / Total time
= (925² / 64) / (925/32)
= 925 /2
= 462.5 ft /sec
Another way
−16t² + 925t = 0
=> -t(16t -925) = 0
=> t = 0 & t = 925/16
Time of flight = 925/16
Max height at = (925/16)/2 = 925/32
h(t) at max height = 925² / 64
Total Distance = 2 * Max height = 925² / 32
Ave speed = (925² / 32)/(925/16) = 925/2
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