On August 4, 2007, NASA's Phoenix Mars Lander was launched into space to search for life in the icy northern region of the planet Mars; it touched down on Mars on May 25, 2008. As the ship raced into space, its jet fuel tanks dropped off when they were used up. The distance one of the tanks falls in t seconds is modeled by the function
s(t) = 16t2
where s is measured in feet per second and t = 0 is the instant the tank left the ship. Use the function s to find the average speed of a tank during the following time intervals.
(a) The first 10 seconds after separation from the ship
_____ ft/s
(b) The first 50 seconds after separation from the ship
_____ ft/s
To find the average speed of the tank during a given time interval, we can calculate the displacement of the tank and divide it by the duration of the interval.
(a) The first 10 seconds after separation from the ship:
To find the displacement, we need to evaluate the function s(t) = 16t^2 over the interval [0, 10]. The displacement is given by s(10) - s(0).
s(10) = 16(10)^2 = 1600 ft/s
s(0) = 16(0)^2 = 0 ft/s
Displacement = 1600 - 0 = 1600 ft/s
Average speed = Displacement / Time interval
Average speed = 1600 ft/s / 10 s
Average speed = 160 ft/s
Therefore, the average speed of the tank during the first 10 seconds is 160 ft/s.
(b) The first 50 seconds after separation from the ship:
Similar to part (a), we need to calculate the displacement over the interval [0, 50]. The displacement is given by s(50) - s(0).
s(50) = 16(50)^2 = 40,000 ft/s
s(0) = 16(0)^2 = 0 ft/s
Displacement = 40,000 - 0 = 40,000 ft/s
Average speed = Displacement / Time interval
Average speed = 40,000 ft/s / 50 s
Average speed = 800 ft/s
Therefore, the average speed of the tank during the first 50 seconds is 800 ft/s.
From a Physics point of view, this question is really flawed.
First of all, it should be -16t^ (gravity works downwards, not upwards)
Secondly, at the moment of jettison of the tanks, the tank still has an upwards velocity, so there should be term in t after the -16t^2
anyway, a "dumb-downed" solution might be
at t = 0 , s(0) = 0 , (not true at all)
at t = 10, s(10) = -16(100) = 1600
avg velocity = (1600=0)/(10-0) = -160 ft/sec
repeat for t = 0 and t = 50