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Ken Carson, 6 feet tall, jumps toward the coward who is 2 feet away. He moves away from the 5‑foot‑tall stage toward the crowd diagonally at 3 feet per second. What is the rate of Ken Carson’s height off the ground in respect to him being only 0.5 feet away from the crowd?
To find Ken Carson’s height off the ground when he is 0.5 feet away from the crowd, we first need to determine how high he is in relation to the crowd based on his jump and position.
Ken’s jump trajectory will create a right triangle where:
– One leg is the horizontal distance from the stage to his position relative to the crowd, which is decreasing as he jumps.
– The other leg is the height difference between the stage and Ken at any point in time.
Since Ken is 6 feet tall and the stage is 5 feet tall, when he jumps towards the crowd, his height doesn’t change; it remains 6 feet. As he is only 0.5 feet horizontally from the crowd, his vertical height from the level of the crowd is:
Height above ground = Ken’s height – Stage height
Height above ground = 6 feet – 5 feet = 1 foot.
Thus, when Ken is 0.5 feet away, he is still 1 foot above the crowd level.
Therefore, the rate of Ken Carson’s height off the ground in respect to being 0.5 feet away from the crowd is 1 foot.
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