"v_0 = 25m\/s"
"t = 1.70s"
Let the body thrown straight up be 1, and the other one be 2
Note that;
"a_y = -g = -\\,10m\/s^2"
"ax = 0\\,m\/s^2"
For body 1
"\\theta"1 = "90\\text{\\textdegree}" (i.e vertical)
"\\begin{aligned}\n\nU_{y1} = v_0sin\u03b8 \\quad &; \\quad U_{x1} = v_0cos\u03b8\\\\\nU_{y1} = 25sin90 \\enspace &; \\quad U_{x1} = 25cos90\\\\\nU_{y1} = 25m\/s \\quad & ;\\quad U_{x1} = 0m\/s\n\n\\end{aligned}"
"\\begin{alignedat}{2}\n\n&x_1 = U_{x1}t\\, &+& \\,0.5a_xt^2\\\\\n&x_1 = 0(1.70)\\, &+&\\, 0.5(0)(1.70)^2\\\\\n&x_1 = 0 + 0\\\\\n\u2234& x_1 = 0m\n\n\\end{alignedat}"
"\\begin{alignedat}{2}\n\n&y_1 = U_{y1}t \\,&+& \\,0.5a_yt^2\\\\\n&y_1 = (25)(1.70) \\,&+&\\, 0.5(-10)(1.70)^2\\\\\n&y_1 = 42.5\\, &-&\\, 14.45\\\\\n\u2234& y_1 = 28.05m\n\n\\end{alignedat}"
For body 2
"\\theta"2 = "60\\text{\\textdegree}"
"\\begin{aligned}\n\nU_{y2} = v_0sin\u03b8 \\quad \\,\\,\\, &; \\quad U_{x2} = v_0cos\u03b8\\\\\nU_{y2}= 25sin60 \\quad & ; \\quad U_{x2} = 25cos60\\\\\nU_{y2}= 21.65m\/s\\,\\, & ; \\quad U_{x2} = 12.5m\/s\n\n\\end{aligned}"
"\\begin{alignedat}{2}\n\n&x_2 = U_{x2}t \\, &+&\\, 0.5a_xt^2\\\\\n&x_2 = 12.5(1.70) \\,&+& \\,0.5(0)(1.70)^2\\\\\n&x_2 = 21.25 &+&\\, 0\\\\\n\u2234 &x_2 = 21.25m\n\n\\end{alignedat}"
"\\begin{alignedat}{2}\n\n&y_2 = U_{y2}t \\,&+&\\, 0.5a_yt^2\\\\\n&y_2 = (21.65)(1.70)\\, &+&\\, 0.5(-10)(1.70)^2\\\\\n&y_2 = 36.81 &-& \\,14.45\\\\\n\u2234&y_2= 22.36m\n\n\\end{alignedat}"
from, distance between 2 points = "\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}"
distance between the 2 bodies = "\\sqrt{(21.25-0)^2+(22.36-28.05)^2}"
= "\\sqrt{(21.25)^2+(-5.69)^2}"
= "\\sqrt{451.56+32.38}"
= "\\sqrt{483.94}"
= "22m"
"\\therefore" the distance between the two bodies is 22m
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