Question

The trajectory of a rock thrown from a height with an initial speed of 19.7 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.

Answer 1

since the refered figure is missing , i will give u a similar example which u can use to understand the solution and use it in your own solution .

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The trajectory of a rock thrown from a height with an initial speed of 16.9 m/s is shown in the figure below. Evaluate the magnitude of the gravitational field at the surface of the planet. The planet has no atmosphere.

solution:

range of object projected at an angle θ
R = (V²/g)sin(2θ)
V is initial velocity in m/s
g is the acceleration of gravity 9.8 m/s²

going from 15 m to 15 m, the range is slightly less than 120 meters, I read it as 119.4 using a lot of magnification. The launch angle I make as arctan (5/6.5) = 37.6º

119 = (16.9²/g)sin(75.1)
119 = (285/g)(0.966)
g = 285•0.966/119 = 2.31 m/s²