1) Aparticle moves in a straight line with the velocity shown in thefigure. Know
ID: 1815287 • Letter: 1
Question
1) Aparticle moves in a straight line with the velocity shown in thefigure. Knowing that x=-540 ft at t = 0, Construct the a-tand x-t curves for 0<t<50 s, and determine the tataldisplacement traveled by the particle when t = 50 s. The twotime at which x =0. 2) In slow pitchsofball the underhand pitch must reach a maximum heifgt of between1.8m and 3.7m above the ground. A pitch is made with aninitial velocity v0 of magnitude 13m/s at an angle of 33 degreewith the horizontal. Determine if the pitch meets the maximumheight requirement, the hieght of the ball as it reaches thebatter. 1) Aparticle moves in a straight line with the velocity shown in thefigure. Knowing that x=-540 ft at t = 0, Construct the a-tand x-t curves for 0<t<50 s, and determine the tataldisplacement traveled by the particle when t = 50 s. The twotime at which x =0. 2) In slow pitchsofball the underhand pitch must reach a maximum heifgt of between1.8m and 3.7m above the ground. A pitch is made with aninitial velocity v0 of magnitude 13m/s at an angle of 33 degreewith the horizontal. Determine if the pitch meets the maximumheight requirement, the hieght of the ball as it reaches thebatter.Explanation / Answer
For (2)
The pitch leaves at V = 13 m/s at an angle of 33 degrees. The x and y vectors of this are:
x(0) = 13 cos (33) = 10.9 m/sec. This doesn'tchange y = 1/2 at^2 + v(y)(0) t + y(0) v(y)(0) is 13 sin(33) = 7.08 m/s a is -9.8 m/sec/sec Maximum y occurs when at +v(y)(0) =0: 7.08 = 9.8t;t = 1.38 seconds This is d/dt of the height, =0 whenit quits changing, which is its max.
Min y must be 1.8 m: 1.8 = 1/2 * (-9.8) * 1.38^2 +1.08 * 1.38 + S(0) = -9.33 + 1.49 + s(0) Will be met only if s(0) is greater than 7.8 meters. That's a really tall pitcher.
Can't determine the height at the batter as you haven't giventhe distance between pitcher and batter. But, you would usethat x value to determine the t when the ball gets there, and putthat in the equation for y
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