This problem can easily be solved by rotating the x and y axes into x' and y' axes. Because of that, the gravity will have both x' and y' components. Let x' be parallel to the slope and in the same sense as the archer's arrow, and y' be perpendicular to the slope and pointing up. The components of gravity are g_y' = 9.8*sin(15), g_x' = 9.8*cos(15). Also, the arrow is shot at an angle 20+15=35 deg above the x' axis.
The total time it takes for a projectile to stay in air is given by:
T = 2*v_y'/g_y' = 2*50*sin(35)/9.8sin(15) = 22.61 s.
The length traveled by the arrow along the slope is the distance it traveled along the x' axis. x' = 1/2*g_x'*T^2 + v_x'*T.
x' = 1/2*9.8cos(15)*22.61^2 + 50cos(35)*22.61x' = 3346 km.
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Answer:
Step-by-step explanation:
Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes
The best and most correct answer among the choices provided by your question is the second choice or letter B.
The information provided by the magazine is <span>reliable because a front-loading washing machine saves 3,000 gallons of water per year and 3000 multiplied by 0.04 is 120.
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Answer: A≈63.62ft²
Step-by-step explanation:
Answer:
The son is 20
The man is 60
Step-by-step explanation:
We can set up this equation with what we know. Let <em>m</em> stand for the Man's current age, and let <em>s</em> stand for his son's current age.
We know the Man's current age is three times that of his son, so this equation can be written as: <em>m = 3s</em>
Ten years ago means the man's current age <em>minus</em> 10 years. So it is <em>m-10</em>. So ten years ago he was 5 times his son's age 10 years ago, <em>5(s-10)</em>
This can be written as: <em>m-10=5(s-10)</em>
Solve with either substitution or elimination, the choice is yours, it doesn't really matter which method you use. I'll be using substitution.
<em>m-10=5(s-10)</em>
<em>3s-10= 5s-50</em>
<em>40=2s</em>
<em>20 = s</em>
The son is <em>20</em> years old.
We know the man is currently 3 times his son's age, because <em>m=3s</em>, so just solve for m since you now know the value of <em>s.</em>
<em>m=3s</em>
<em>m=3(20)</em>
<em>m=60</em>
The man is <em>60</em> years old
