How Is Displacement Calculated in Projectile Motion on Mars?

[Delta G]

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

 

[xcvxcvvc]

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.

 

[kerimek]

To find the magnitude of displacement, we need to find the distance between the first and last reading. We can use the equation x = x0 +vox*t to find the distance traveled in the x-direction. We know that the probe has an initial horizontal velocity of 53.84 m/s, and it travels for a total time of 9.952 s. Plugging in these values, we get x = 0 + (53.84 m/s)(9.952 s) = 535.023 m.

To find the distance in the y-direction, we can use the equation y = y0 + v0y*t +1/2*at^2. We know that the probe starts at a height of 3000 m and lands at a height of 0 m, so the change in height is 3000 m. We also know that the probe has an initial vertical velocity of 0 m/s, and the acceleration due to gravity on Mars is approximately 3.711 m/s^2. Plugging in these values, we get y = 3000 m + (0 m/s)(9.952 s) + 1/2(3.711 m/s^2)(9.952 s)^2 = 3000 m - 183.392 m = 2816.608 m.

To find the magnitude of the displacement, we can use the Pythagorean theorem: d = √(x^2 + y^2) = √(535.023 m^2 + 2816.608 m^2) = √(3358464.389) ≈ 1833.645 m.

Therefore, the correct answer is c. 3536 m.