Answer to Question #166001 in Astronomy | Astrophysics for wadzani

Question #166001
a stone propelled from a catapault with a speed of 50m/s attains a height
of 100 m. calculate;the time of flight,the angle of projection,the range attained
1
Expert's answer
2021-02-24T12:49:51-0500


a) Time of flight for a projectile, "T=2Usin\\frac{\\theta}{g}"

"U = 50 m\/s"

"\\theta = ?"

"g = 10 m\/s^2"

However, maximum height, "H = U^2sin^2""\\frac{\\theta}{2g}"

"H = 100 m"

Hence, "100 = 50^2 sin^2\\frac{\\theta}{2\\times10} \n\n\u200b"

"sin^2\\theta = \\frac{2\\times10\\times100}{50^2}= 0.8"

"sin\\theta = 0.8944"

Therefore, "T = \\frac{2\\times50\\times0.8944}{10} = 8.9 s"

b) "sin\\theta = 0.8944"

Using Natural Sine Table (Trigonometrical Tables)

"\\theta", angle of projection = 63,4o1'

c) Range, "R = \\frac{U^2sin2\u03b8}{g} = \\frac{50^2sin(2\\times63.4^o1')}{10} = 250 \\times 0.8007 = 200.2 m"

Answer: a) T = 8.9 s; b) "\\theta" = 63,4o1'; c) R = 200.2 m.


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