Sivakumar MATH 171
Exercise Set 6
0.
Study all the worked examples in the text.
1.
If a snowball melts so that its surface area decreases at a rate of 1 square centimetre per minute, find the rate at which the diameter decreases when the diameter is 10 cm.
2.
A spotlight on the ground shines on a wall 12 metres away. If a man 2 metres tall walks from the spotlight toward the building at a speed of 1 .
6 metres per second, how fast is his shadow on the building decreasing when he is 4 metres from the building?
3.
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm?
4.
A man starts walking north at 4 ft/sec from a point P . Five minutes later a woman starts walking south at 5 ft/sec from a point 500 feet due east of P . At what rate are the people moving apart 15 minutes after the woman starts walking?
5.
A kite 100 feet above the ground moves horizontally at a speed of 8 ft/sec. At what rate is the angle between the string and the horizontal decreasing when 200 feet of string have been let out?
6.
A runner runs around a circular track of radius 100 metres at a constant speed of 7 m/sec.
The runner’s coach is standing at a distance 200 metres from the centre of the track. How fast is the distance between them changing when the distance between them is 200 metres?
7.
Let P
0 x
2
+ y
2 denote the fixed point (2 , 3).
Suppose that a particle P moves along the circle
= 2 in the anticlockwise direction, from the point (
√
2 , 0) towards the point (0 ,
√
2).
The distance between P and the y -axis is changing at a rate of 1 unit per second. Find the rate at which the distance between P and P
0 changing, at the instant when P crosses the line y = x .
Other questions from the text: pages 219-221 – 9,10,15,16,17,23,27,29,31,32
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