Final answer:
To determine the horizontal distance the kite has traveled after 30 seconds, multiply the time by the horizontal speed. Calculate the angle of elevation from the child to the kite after 15 seconds by finding the horizontal distance and using the tangent function. The speed of the kite is equal to its horizontal speed if it remains at a constant height. The tension force in the kite string can be calculated using the mass and acceleration.
Step-by-step explanation:
a) To determine the horizontal distance the kite has traveled after 30 seconds, we need to calculate the distance it has traveled horizontally. Since the height remains constant, the horizontal distance is equal to the product of the time and the horizontal speed. If we assume that the kite is not affected by any horizontal forces such as wind resistance, the horizontal speed remains constant. Therefore, the horizontal distance traveled would be 30 seconds multiplied by the horizontal speed of the kite.
b) To calculate the angle of elevation from the child to the kite after 15 seconds, we need to consider the vertical and horizontal components of the kite's position. The vertical distance remains constant at 200 ft, so we can calculate the horizontal distance using the equation: horizontal distance = time * horizontal speed. Once we have the horizontal distance, we can use it to calculate the angle of elevation using the tangent function.
c) If the kite remains at a constant height, its vertical speed remains zero. So, the speed of the kite would be equal to its horizontal speed. We can calculate the horizontal speed by dividing the horizontal distance traveled by the time.
d) The tension force in the kite string can be calculated using the equation: tension force = mass * acceleration, where the mass of the kite is equal to its weight divided by the acceleration due to gravity.