The picture shows the graphs of three functions of a moving car: one is the posi

Question

The picture shows the graphs of three functions of a moving car: one is the position function, one is the velocity function, and the other is the acceleration function. Identify which curve is the position function. graph A graph B graph C Not enough information to determine. A small boy standing in a flat field watches a balloon rise in the distance. The balloon leaves the ground 500 m away from the boy and rises vertically at the rate of 7 m/minute. At what rate is the angle of inclination of the boy's line of sight (ANGLE in radians) increasing at the instant when the balloon is exactly 500 m above the ground? 7/500 radians/minute 7/1000 radians/minute 14/500 radians/minute 14/250 radians/minute None of the above. A woman standing on a cliff is watching a boat through a telescope as the boat approaches a dock on the shoreline directly below her. If the telescope is 250 meters above the water level and if the boat is approaching at 20 meters/second, at what rate is the angle of the telescope changing when the boat is 100 meters from shore? 0.049 radians/second -0.049 radians/second 0.079 radians/second -0.079 radians/second None of the above.

Explanation / Answer

1)C there is only one graph that is negative.so it must be acceleration graph.because if velocity becomes negative then obviously at some point acceleration is negative so A is acceleration.and C increases even when acceleration is negative.so it must be position.Hence Graph C is position graph 2)B h=500tanx(h is height and x is angle of elevation) dh/dt=500sec^2(x)dx/dt so dx/dt=7/1000

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