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PHY 201
Your 'cq_1_08.2' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** CQ_1_08.2_labelMessages **
A ball is tossed upward at 15 meters / second from a height of 12 meters above the ground. Assume a uniform downward acceleration of 10 m/s^2 (an approximation within 2% of the 9.8 m/s^2 acceleration of gravity).
• How high does it rise and how long does it take to get to its highest point? answer/question/discussion: maximum height the velocity is going to be 0. vf = 0, v0 = 15m/s, a = -10m/s^2. vf = 0, v0 = 15m/s, a = -10m/s^2. -10m/s^2 = -15m/s / `dt. `dt = -15m/s / (-10m/s^2). `dt = 1.5 sec (it takes 1.5 seconds to get to its highest point). vAve = `ds / `dt. 7.5m/s * 1.5 sec = `ds. `ds = 11.25m (it rises 11.25 meters). #$&*
• How fast is it then going when it hits the ground, and how long after the initial toss does it first strike the ground? answer/question/discussion: highest point is 11.25m + 12m = 32.25m. v0 = +15m/s. `ds = -12m. a = -10m/s^2. vf^2 = v0^2 + 2a `ds. vf^2 = (15m/s)^2 + 2(-10m/s^2) * -12m. vf^2 = 225m^2/s^2 + 240m^2/s^2. sqrt(vf^2) = sqrt(465m^2/s^2). vf = -21.56m/s (the balls velocity when it hits the ground is -21.56m/s). -3.28m/s = -12m / `dt. `dt = 3.6sec. .#$&*
• At what clock time(s) will the speed of the ball be 5 meters / second? answer/question/discussion: vf = 5m/s. v0 = 15m/s. a = -10m/s^2. -10m/s = 10m/s / `dt. `dt = 1 sec. #$&*
• At what clock time(s) will the ball be 20 meters above the ground?
• How high will it be at the end of the sixth second?answer/question/discussion: position must change by 8 meters (20-12=8). `ds = 8m. a = -10m/s^2. v0 = 15m/s. vf^2 = v0^2 + 2a `ds. vf^2 = (15m/s)^2 + 2(-10m/s^2) * 8m. vf^2 = 225m^2/s^2 + -160m^2/s^2. sqrt(vf^2) = sqrt(65m^2/s^2). vf = 8.06m/s. -10m/s^2 = -6.94m/s / `dt. `dt = 0.694sec ( the clock will be at .694sec when the ball is 20 meters above the ground). `dt = 6 sec. a = -10m/s^2. v0 = 15m/s. vf = v0 + a `dt. vf = 15m/s + -10m/s^2 *6sec. vf = 15m/s + -60m/s. vf = -45m/s. vAve = (-45m/s + 15m/s) / 2 = -15m/s. `ds = -15m/s * 6sec. `ds = -90m/s + 12. `ds = -78m. #$&*
&#Good responses. Let me know if you have questions. &#