How fast is the ball moving just as it lands? One way to measure g on another pl

Question

How fast is the ball moving just as it lands? One way to measure g on another planet or moon by remote sensing is to measure how long it takes an object to fall a given distance. A lander vehicle on a distant planet records the fact that it takes 4.50 s for a ball to fall freely 12.52 m, starting from rest.

A. What is the acceleration due to gravity on that planet? Express your answer in m/s^2.

B. What is the acceleration due to gravity on that planet? Express your answer in earth g’s.

C. How fast is the ball moving just as it lands?

Explanation / Answer

distance = (initial velocity)(time) + (1/2)(acceleration)(time)^2

12.52 = (0)(4.50) + (1/2)a(4.50)^2

12.52 = (1/2)a(4.50)^2

a)

a = 2(12.52) / (4.50)^2 = 1.236 m/s^2
b)

Since 1g =9.8 m/s^2, a =1.236/9.8 = .1261g

c)

The speed of the ball just as it lands can be found using the equation

final velocity = initial velocity + acceleration(time)

v = 0 +1.236(4.50) = .274 m/s

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