1. Consider a three-dimensional coordinate system in which a dart is projected at position (x0, Yo, 2o) along direction (a, b, c) with initial speed vo ft/s. Here we assume that yYo < 0 and b > 0, so that the dart is projected towards the positive y axis. Write a computer program that takes inputs x0, Y0, 20, a, b, c, vo and computes the time and location at which the dart would hit the xz-plane.

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1. Consider a three-dimensional coordinate system in which a dart is projected at
position (xo, Yo, zo) along direction (a, b, c) with initial speed vo ft/s. Here we
assume that Yo < 0 and b > 0, so that the dart is projected towards the positive y
axis. Write a computer program that takes inputs xo, Y0, Z0, a, b, c, vo and computes
the time and location at which the dart would hit the xz-plane.
Transcribed Image Text:1. Consider a three-dimensional coordinate system in which a dart is projected at position (xo, Yo, zo) along direction (a, b, c) with initial speed vo ft/s. Here we assume that Yo < 0 and b > 0, so that the dart is projected towards the positive y axis. Write a computer program that takes inputs xo, Y0, Z0, a, b, c, vo and computes the time and location at which the dart would hit the xz-plane.
2. Assume that there exists a high-speed sensor that could capture the location of
the dart at specific times. Suppose that the sensor captures a series of locations
(T1, Y1, 21), ..., (xN, YN, 2N) at t1,...,tN seconds. Namely, through the sensor are
able to make N observations on the location, and at the i-th observation we know
the exact location of the dart (x;, Yi, z;) at time t;. Based on the observed data and
your derivation in the previous question, can you predict the time and location at
which the dart would hit the xz-plane?
Transcribed Image Text:2. Assume that there exists a high-speed sensor that could capture the location of the dart at specific times. Suppose that the sensor captures a series of locations (T1, Y1, 21), ..., (xN, YN, 2N) at t1,...,tN seconds. Namely, through the sensor are able to make N observations on the location, and at the i-th observation we know the exact location of the dart (x;, Yi, z;) at time t;. Based on the observed data and your derivation in the previous question, can you predict the time and location at which the dart would hit the xz-plane?
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