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Check yourself Answers

1Let d be the distance between A and B and t1, t2 the travel times back and forth. Then d = 15 t1 = 30 t2, i.e. t1 = 2 t2. The average speed is then v¯=2 d t 1+t 2=2×30 t 2 3 t 2=20 m s−1

2Positive for 1.0 s on, because curve is concave up, negative for 0 s to 1.0 s and zero at 1.0 s.

3It takes 2 s to get to the maximum height and 2 to return so the required time is 4 s.

4 aZero at about 0.4 s and 1.6 s.

bNegative from 0.4 s to 1.6 s.

cMost negative at 1.0 s.

dThe displacement from 0 s to 1.0 s is about the same in magnitude as that from 1.0 s to 2.0 s so the displacement at 2.3 s will be positive.

5 K=1 2 m u 2. At the highest point, K E=1 2 m u 2 cos 2⁡60°=1 2 m u 2×1 4=K 4.

6Both H and R are inversely proportional to the acceleration of free fall and so both are halved.