a model rocket shot up a to a point 20 m above the ground, hitting a smokestack, and then dropped straight down to a point 11 m from its launch site. Find to the nearest meter the total distance traveled from launch to touchdown
To find the total distance traveled from launch to touchdown, we need to calculate the sum of the vertical distance traveled during the ascent and descent, as well as the horizontal distance traveled.
Given:
Vertical distance traveled during ascent = 20 m
Vertical distance traveled during descent = 0 m (since it drops straight down)
Horizontal distance traveled = 11 m
To calculate the total distance, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle (in our case, the total distance) is equal to the sum of the squares of the other two sides.
Let's denote the total distance traveled as d.
Using the Pythagorean theorem:
d^2 = (20^2 + 11^2)
Simplifying the equation:
d^2 = 400 + 121
d^2 = 521
Taking the square root of both sides:
d = sqrt(521)
d ≈ 22.82
Rounding to the nearest meter, the total distance traveled from launch to touchdown is approximately 23 meters.
To find the total distance traveled by the model rocket from launch to touchdown, we need to calculate the horizontal distance traveled and the vertical distance traveled separately, and then find the hypotenuse of the triangle formed by these distances using the Pythagorean theorem.
Let's start by calculating the horizontal distance traveled. We are given that the rocket dropped straight down to a point 11 m from its launch site. This means that the horizontal distance traveled is equal to the distance from the launch site to the point directly below the smokestack.
Next, we need to calculate the vertical distance traveled. The rocket started at ground level and went up to a point 20 m above the ground. Therefore, the vertical distance traveled is equal to 20 m.
Now, we can find the total distance traveled using the Pythagorean theorem:
Total distance traveled = √(horizontal distance)^2 + (vertical distance)^2
Plugging in the values:
Total distance traveled = √(11^2 + 20^2)
Calculating this:
Total distance traveled ≈ √(121 + 400) ≈ √(521) ≈ 22.83
Rounding to the nearest meter, the total distance traveled from launch to touchdown is approximately 23 meters.
20 = V^(2sin^µ)/2g and
11 = V^(2sin2µ)/g
V = initial velocity
µ = angle of elevation above horizontal
g = acceleration due to gravity
Solve each for V and equate the results.
Solve for µ.