quiz4soln

# quiz4soln - 2 We know that we have two equations for the...

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MATH 231 / Spring 2008 February 13, 2008 Name: Key 1. (3 points) For a smooth space curve r ( t ) with smooth derivative, give the equations for T ( t ), N ( t ), and B ( t ). Solution: T ( t ) = r 0 ( t ) | r 0 ( t ) | N ( t ) = T 0 ( t ) | T 0 ( t ) | B ( t ) = T ( t ) × N ( t ) 2. (7 points) A batter hits a baseball 3 ft above the ground toward the center ﬁeld fence, which is 10 ft high and 400 ft from home plate. The ball leaves the bat with speed 100 ft/s at an angle 45 above the horizontal. Does the ball clear the fence? Solution: Recall that g = 32 . 2 ft/s
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Unformatted text preview: 2 . We know that we have two equations for the trajectory of the ball: x = 100 t cos 45 ◦ y = 100 t sin 45 ◦-1 2 gt 2 + 3 Solving for when x = 400, we ﬁnd that t = 4 √ 2. Plugging this into the equation for y , we ﬁnd that y ≈ 100(4 √ 2) 1 √ 2-1 2 32 . 2(4 √ 2) 2 + 3 =-112 . 2 ft Thus, we know that the ball does not clear the fence (nor does it come anywhere close, for that matter). 1...
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