P2F11-Week4-Barwick

P2F11-Week4-Barwick - P2 Week 4 Motion in One Dimension...

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P2 Week 4 ü࿏ Motion in One Dimension with constant acceleration ü࿏ Graphical methods ü࿏ Differentiation, slopes, maxima and minima
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Summary for constant acceleration linear motion x-x 0 t-t 0 v v 0 a Equation v = v o + a " (t - t 0 ) x - x 0 = 1 2 v + v o ( ) (t - t 0 ) x " x o = v o (t - t 0 ) + 1 2 a (t - t 0 ) 2 v 2 = v 0 2 + 2 a x " x o ( )
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y-y 0 t-t 0 v v 0 a Equation Summary for freely falling objects Up is positive Hence acceleration due to gravity = – g g is the magnitude of acceleration due to gravity Average sea-level value for g =9.8m/s 2 . v = v o " g # (t - t 0 ) y " y o = v o (t - t 0 ) " 1 2 g (t - t 0 ) 2 v 2 = v 0 2 " 2 g y " y o ( ) y - y 0 = 1 2 v + v o ( ) (t - t 0 )
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Clicker problem Raindrops fall 2 km from a cloud to the ground. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Take g=10m/s 2 . A: 70 km/hr B: 140 km/hr C: 500 km/hr D: 720 km/hr E: 900 km/hr
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Clicker problem Raindrops fall 2 km from a cloud to the ground. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Take g=10m/s 2 . Use v 2 =v 0 2 +2 × 10 × 2000 m 2 /s 2 . Set v 0 =0. So |v|=200 m/s = 200 × 3600 s / 1000 m × km/hr = 720 km/hr Having drops fall on your head at this speed would be quite dangerous! Large raindrops hit terminal speeds of about 40 km/hr in the air.
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Strategy Precise answers usually require algebraic solutions Write out equations and solve for unknown However, more vaguely worded problems may best be solved graphically (See next few problems). Increase, Bigger, smaller, faster, shorter rather than how big, how fast, how small
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Clicker question How does the vertical distance between them change? A: increases B: decreases C: stays the same How does the difference in their velocities change? A: increases B: decreases C: stays the same A skydiver jumps out of a hovering helicopter. A few seconds later, another skydiver jumps out, so they both fall along the same vertical line relative to the helicopter. Both sky divers fall with the same acceleration. Assume that g is constant.
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Clicker question A skydiver jumps out of a hovering helicopter. A few seconds
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