QuestionJuly 25, 2025

A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.35 radians (That is, the rocket's path and the ground form an angle measuring 1.35 radians.) a. What is the slope of the rocket's path? square b. If the rocket has traveled 55 yards horizontally since it was launched, how high is the rocket above the ground? square yards c. At some point in time the rocket is 405 yards above the ground. How far has the rocket traveled horizontally (since it was launched) at this point in time? square yards

A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.35 radians (That is, the rocket's path and the ground form an angle measuring 1.35 radians.) a. What is the slope of the rocket's path? square b. If the rocket has traveled 55 yards horizontally since it was launched, how high is the rocket above the ground? square yards c. At some point in time the rocket is 405 yards above the ground. How far has the rocket traveled horizontally (since it was launched) at this point in time? square yards
A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.35 radians (That is, the rocket's path and the ground form an angle measuring 1.35 radians.) a. What is the slope of the rocket's path? square b. If the rocket has traveled 55 yards horizontally since it was launched, how high is the rocket above the ground? square yards c. At some point in time the rocket is 405 yards above the ground. How far has the rocket traveled horizontally (since it was launched) at this point in time? square yards

Solution
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Answer

a. Slope = 4.743 ### b. Height = 260.865 yards ### c. Horizontal distance = 85.37 yards Explanation 1. Calculate the slope of the rocket's path The slope m is given by \tan(\theta), where \theta = 1.35 radians. Thus, m = \tan(1.35). 2. Calculate the height after traveling 55 yards horizontally Use the formula for height: h = m \times \text{horizontal distance}. Here, h = \tan(1.35) \times 55. 3. Calculate horizontal distance when 405 yards above ground Rearrange the height formula to find horizontal distance: \text{horizontal distance} = \frac{\text{height}}{m}. So, \text{horizontal distance} = \frac{405}{\tan(1.35)}.

Explanation

1. Calculate the slope of the rocket's path<br /> The slope $m$ is given by $\tan(\theta)$, where $\theta = 1.35$ radians. Thus, $m = \tan(1.35)$.<br /><br />2. Calculate the height after traveling 55 yards horizontally<br /> Use the formula for height: $h = m \times \text{horizontal distance}$. Here, $h = \tan(1.35) \times 55$.<br /><br />3. Calculate horizontal distance when 405 yards above ground<br /> Rearrange the height formula to find horizontal distance: $\text{horizontal distance} = \frac{\text{height}}{m}$. So, $\text{horizontal distance} = \frac{405}{\tan(1.35)}$.
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