A target is fixed on top of a pole 13m high. a man is standing at a distance 50m from the pole is capable of projecting a stone with velocity 10√g m/s. if he wants to wants to strike the target at shortest possible time, at what angle should he project the stone???????
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The faster the stone is thrown it quicker it reaches the target. So let us say:
u = 10√g x = 50 m y = 13 m Ф = angle wrt horizontal.
x = u cosФ t => t = 50 secФ / u
y = u sin Ф t - g t² /2
13 = 50 tanФ - 12.5 sec² Ф
=> 12.5 tan²Ф - 50 tan Ф + 25.5 = 0
=> tan²Ф - 4 tanФ + 2.04 = 0
=> tanФ = 2 + - 1.4
=> tanФ = 3.4 or 0.6
=> Ф = 73.6° or 30.96°
That is the answer: 30.96°
Angle made by the straight line connecting the target and the man
= Tan⁻¹ (13/50) = 14.5 °
time taken = 50 * √(1+3.4²) /(10√g) = 5√(12.56 /g) sec
u = 10√g x = 50 m y = 13 m Ф = angle wrt horizontal.
x = u cosФ t => t = 50 secФ / u
y = u sin Ф t - g t² /2
13 = 50 tanФ - 12.5 sec² Ф
=> 12.5 tan²Ф - 50 tan Ф + 25.5 = 0
=> tan²Ф - 4 tanФ + 2.04 = 0
=> tanФ = 2 + - 1.4
=> tanФ = 3.4 or 0.6
=> Ф = 73.6° or 30.96°
That is the answer: 30.96°
Angle made by the straight line connecting the target and the man
= Tan⁻¹ (13/50) = 14.5 °
time taken = 50 * √(1+3.4²) /(10√g) = 5√(12.56 /g) sec
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