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MAVERICK [17]
3 years ago
15

A medieval prince trapped in a castle wraps a message around a rock and throws it from the top of the castle with an initial vel

ocity of 12m/s[42 degrees of above the horizontal]. The rock lands just on the far side of the castle's moat, at a level 9.5m below the initial level. Determine the rock's time of flight. ...?
Physics
1 answer:
andrey2020 [161]3 years ago
5 0
Vertically we can say 
<span>Vertical acceleration = - g </span>
<span>Vertical velocity = u sinѲ - gt [Ѳ = 42; u = 12 m/s] </span>
<span>Vertical displacement = u sinѲt - (1/2) g t^2 + 9.5 </span>

<span>When the rock hits the ground, its vertical displacement will be zero. So we can say.. </span>

<span>u sinѲt - (1/2) g t^2 + 9.5 = 0 </span>
<span>I'll rearrange this .... </span>

<span>- (1/2) g t^2 + u sinѲt + 9.5 = 0 </span>

<span>Can you see that we now have a quadratic in t? </span>

<span>Using the well known formula </span>

<span>t = [ - u sinѲ ± √( u^2 sin^2Ѳ - 4(( - (1/2)g * 9.5))] / (- g) </span>

<span>t = [- u sinѲ ± √( u^2 sin^2Ѳ + 19g)] / (-g) </span>

<span>t = [- 8.03 ± √(250.86)] / (-9.81) </span>

<span>t = [- 8.03 ± 15.84] / (-9.81) </span>

<span>t = (- 8.03 + 15.84) / (-9.81) or t = (-8.03 - 15.84) / (-9.81) </span>

<span>t = - 0.8 or t = 2.43 </span>

<span>Well, a negative time has no meaning so </span>
<span>t = 2.43 seconds. </span>
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