A body is projected downwards at angle 30 to horijontal and velocity 9.8 from top oftower 29.4 m high how long it take befores strike ground
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let
Ɵ = 30°
U = 9.8m/s
From the figure,
for vertical motion,
Uy = Usin30 = 9.8×1/2 = 4.9 m/s
ay = -g = -9.8m/s²
Sy = -29.4m
t = T = ?
Sy = UyT + ayT²/2
-29.4 = 4.9×T + (-10)T²/2
-29.4 = 4.9×T - 5T²
9.8T² - 4.9T - 29.4 = 0
4.9(2T²-T-6) = 0
2T² - T - 6 = 0
2T² -4T+3T - 6 = 0
2T(T-2)+3(T-2) = 0
(T-2)+(2T+3) = 0
T = 2
or
T = -3/2
but T always positive
T = 2s
Ɵ = 30°
U = 9.8m/s
From the figure,
for vertical motion,
Uy = Usin30 = 9.8×1/2 = 4.9 m/s
ay = -g = -9.8m/s²
Sy = -29.4m
t = T = ?
Sy = UyT + ayT²/2
-29.4 = 4.9×T + (-10)T²/2
-29.4 = 4.9×T - 5T²
9.8T² - 4.9T - 29.4 = 0
4.9(2T²-T-6) = 0
2T² - T - 6 = 0
2T² -4T+3T - 6 = 0
2T(T-2)+3(T-2) = 0
(T-2)+(2T+3) = 0
T = 2
or
T = -3/2
but T always positive
T = 2s
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