Drag Race #1 Given: Dx= meters in Dt= sec.

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Presentation transcript:

Drag Race #1 Given: Dx= 402 .34 meters in Dt=11.963 sec. Unknown: vavg=?? Principle: Kinematics(where to look for eq’n) Picture: Equation: Simplify/Solve/Substitute

Drag Race #2 Given: vf= 40.73 m/s in Dx=201.17m Unknown: aavg=?? Principle: Kinematics(where to look for eq’n) Picture: Equation: Simplify/Solve/Substitute

Aircraft Catapult(v) v(m/s) 50 time(s) 5

Aircraft Catapult(a) a(m/s2) 20 time(s) 5 To draw accel; Get slope of each range of velocity graph 0-2 sec Slope = (60-10)/2=25 2-5 sec Slope=zero time(s) 5

Aircraft Catapult(x) x(m) 300 200 100 time(s) 5 To draw position analyze each portion of the velocity graph 0-2 sec Area=(1/2)(2.0)(60-10)+10(2.0)=1/2(60+10)(2.0)=70 Concave up since velocity is increasing 2-5 sec Area=60(5.0-2.0)=180, straight line since velocity is constant time(s) 5

Freefall Example 1) A ball is dropped from 10 meters high. How fast is it going when it hits the ground? 2) How long does it take to reach the ground? 1. vf2=v02+2a(hf-h0) Vf=+/-sqrt(2g(hf-h0)) Vf=+/-sqrt(-19.6(0-10))=+/-14m/s Significance of +/- is …+ solution is when ball was thrown up to reach 10 meters high with zero velocity Neg solution is the one we want, negitive velocity at the ground, THE EQUATION DOES NOT KNOW, that we held it first, then dropped it! 2. time=(v-v0)/a =-14/(-9.8)=1.4 sec

Freefall Example 3) A ball is given an upward velocity of 5.0 m/s, what is the maximum height it will reach? 4) How long does it take to reach this max height? 3. Hmax=-v02/2a=-25/(-19.6)=1.3m 4. t=(vf-v0)/a=-5.0/-9.8=0.51 sec

Freefall Example 5) A ball is thrown upward with a velocity of 4.0 m/s. How fast is it going when it hits the ground, 10 meters below where it was thrown from? 1. vf2=v02+2a(hf-h0) Vf=+/-sqrt(v02+2g(hf-h0)) Vf=+/-sqrt(16-19.6(0-10))=+/-14.6m/s

Freefall Cases Downy Uppy Uppy – downy Dropping or “spiking” Toss up Toss up off a ledge, object lands lower than the ledge Establish your coordinate system and be consistent with signs.

More examples More example problems Try: v0=-3.0, a=5, Dt=4, Dx=? Try a “spike” (as in football player’s touchdown celebration) xf=-5.0, x0=2.0, v0=-1.0, a=-9.8, Dt=? 60 meters 0.69 sec