3 GravitySigns are always how you start e.g. if you start throwing upwards, then up is + Acceleration is g and always down. Sign depends on if you say up is + or down is +. Watch for displacement e.g. throwing something off a cliff 30 m above ground, hence displacement is -30
4 Example 3.1 [LC:1988 Q1 (b)]A particle falls freely from rest from a point o, passing three points a, b and c, the distances ab and bc being equal. If the particle takes 3 s to pass from a to b and 2 s from b to c, calculate |ab|
5 Always go from A as initial velocity remains same +Au=uxA to CA to BB2xu=u, a=g, s=x, t=3u=u, a=g, s=2x, t=5CDown is positivehence g ispositive hereSolve to give x =147 m
6 Example 3.2 [LC:2002 Q1(a)]A stone is thrown vertically upwards under gravity with a speed of u m/s from a point 30 m above the horizontal ground. The stone hits the ground 5 s later.Find the value of uFind the speed with which it hits the ground.
7 Displacement is -30 because up is positive u=+ua=-gs=-30t=5+-30Finding vFinding u
8 Example 3.3 [LC:1990 Q1(a)]A particle is projected vertically upwards with velocity u m/s and is at a height h after t1 and t2 seconds respectively. Prove that:
9 u=+ua=-gs=+ht=t (t1 on way up, t2 on way down)hSolving+Product of 2 rootsRemember α and β
10 Example 3.4 [LC:1992 Q1(a)]A balloon ascends vertically at uniform speed. 7.2 seconds after it leaves the ground, a particle is let fall from the balloon. The particle takes 9 seconds to reach the ground. Calculate the height from which the particle was dropped.
11 Balloon+uhFor the Particleu= +ua= -9.8t= 9s= -h
13 Equations always give zero to n time 3rd second is between t=2 seconds and t=3 secondsEquations always give zero to n timeLet x = distance travelled in first 3 secondsLet y = distance travelled in first 2 secondsFrom the Question