A Projectile Is Launched Vertically Upward from the Surface of Mars

question 50

Essay

A projectile is launched vertically upward from the surface of Mars. The table below gives the height of the object at the indicated time following launch. $$\begin{array}{l}\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Time (seconds): } & 0 & 0.4 & 0.8 & 1.2 & 1.6 & 2.0 & 2.4 & 2.8 & 3.2 & 3.6 \\\hline \text { Height (feet): } & 0 & 18.2 & 34.4 & 48.4 & 60.4 & 70.4 & 78.3 & 84.2 & 88.1 & 90.0 \\\hline\end{array}\\\\\begin{array} { | l | c | c | c | c | c | c | c | c | c | c | } \hline \text { Time (seconds): } & 4.0 & 4.4 & 4.8 & 5.2 & 5.6 & 6.0 & 6.4 & 6.8 & 7.2 & 7.6 \\\hline \text { Height (feet): } & 89.6 & 87.3 & 82.9 & 76.5 & 68.1 & 57.6 & 45.1 & 30.5 & 13.8 & 0 \\\hline\end{array}\end{array}$$
(a) Graph the data.
(b) Using the data, compute the average velocity of the projectile on the following time intervals:
(i) [0; 4.0]
(ii) [0.8; 3.2]
(iii) [1.2; 2.8]
(iv) [1.6; 2.4]
(v) [2.0; 2.4]
(vi) [1.6; 2.0]
(c) Estimate the velocity of the projectile when t = 2.0. Justify your results.(d) Using your graph and the table of values, determine when the projectile reaches its maximum height. Justify your answer.(e) Using the graph and table of values, estimate the velocity of the projectile throughout the interval [0; 7.6] and sketch a graph of this velocity.

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