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Answer:
10 ft/s and 6.818 mi/hr
Explanation:
We can represent the situation with the following diagram:
When the angle is 63 degrees, the value of h can be calculated using a trigonometric function as:
[tex]\tan 63=\frac{h_i}{100}[/tex]Because h is the opposite side and 100 ft is the adjacent side. Solving for h, we get:
[tex]\begin{gathered} h_i=100\times\tan 63 \\ h_i=196.26\text{ ft} \end{gathered}[/tex]In the same way, when the angle is 67.9 degrees, we can calculate the height as follows:
[tex]\begin{gathered} \tan 67.9=\frac{h_f}{100} \\ h_f=100\times\tan 67.9 \\ h_f=246.27ft \end{gathered}[/tex]Now, we can calculate the speed in ft per second as follows:
[tex]s=\frac{h_f-h_i}{t}=\frac{246.27ft-196.24ft}{5s}=10\text{ ft/s}[/tex]Finally, 1 mile = 5280 ft and 1 hour = 3600 seconds, so we can convert to miles per hour as:
[tex]10\text{ ft/s }\times\frac{1\text{ mile}}{5280\text{ ft}}\times\frac{3600}{1\text{ hour}}=6.818\text{ mi/hr}[/tex]Therefore, the answers are:
10 ft/s and 6.818 mi/hr
