How Is Displacement Calculated in Projectile Motion on Mars?

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SUMMARY

The displacement of a space probe landing on Mars, with an initial horizontal velocity of 53.84 m/s and telemetry readings recorded every 9.952 seconds, is calculated using the formula for displacement in projectile motion. The readings indicate an initial altitude of 3000 m and a final altitude of 165.0 m, resulting in a vertical displacement of 2835 m. By applying Pythagoras's theorem to combine the horizontal and vertical components, the total displacement is determined to be 4397 m, confirming option a as the correct answer.

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Homework Statement



Telemetry for a remote space probe is the ability to measure altitude using radar. A probe with initial horizontal velocity of 53.84 m/s descends on Mars. During the landing attempt, the telemetry readings are relayed to Earth every 9.952 s. The sequence received is: 3000 m, 2921 m, 2685 m, 2291 m, 1740 m, 165.0 m, touchdown. What is the magnitude of the displacement between the first and last reading?

a. 4397 m
b. 161,521 m
c. 3536 m
d. 3000 m

Homework Equations



vy^2 = v0^2 +2ay
vy = v0y +at
x = x0 +vox*t
y = y0 + v0y*t +1/2*at^2

The Attempt at a Solution


 
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Displacement is a vector. Although you can quickly say that the horizontal component of the displacement is 3000, that is not the answer. You must use the horizontal velocity paired with the total time to find an x component of displacement. Using Pythagoras's theorem, find the hypotenuse of the two components.
 

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