A jumping spider jumps from a log onto the ground below. Its height, h, in centimetres, as a function of time, t, in seconds, since it jumped can be modelled by the function h(t) = -490t2 + 75t + 12. Where appropriate, answer the following questions to the nearest tenth.
a) Graph the function.
b) What does the h-intercept represent?
c) When does the spider reach its maximum height? What is its maximum height?
d) When does the spider land on the ground?
e) What domain and range are appropriate in this situation?
f) What is the height of the spider 0.05 s after it jumps?
+33658 I answered the first few parts of this one here: http://web2.0calc.com/questions/a-jumping-spider-jumps-from-a-log-onto-the-ground-below-its-height-h-in-centimetres-as-a-function-of-time-t-in-seconds-since-it-jumpe
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+23254 a) Graph it, either byhand or by calculator.
b) The h-intercept represent the height of the log.
c) The maximum height occurs at about 0.0765 secs. The maximum height is about 14.87 cm. These are the coordinates of the vertex of the funtion.
d) The spider lands after approximately 0.251 seconds.
e) Appropriate domain: [0, 0.251] Appropriate range: [0, 14.87]
f) Replace t with 0.05 to get 14.525 cm.
+33658 I answered the first few parts of this one here: http://web2.0calc.com/questions/a-jumping-spider-jumps-from-a-log-onto-the-ground-below-its-height-h-in-centimetres-as-a-function-of-time-t-in-seconds-since-it-jumpe
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