An object on a planet has a mass of 243 kg. What is the acceleration of the object, if the radius of the planet is 2.32 x 10^7 m, and the mass of planet is
6.35 x 10^30 kg? Estimate G as 6.67 x 10^-11 N (m/kg)^2

The acceleration of the object is

The gravitational acceleration of object is computed by formula shown below,

Where G is gravitational constant, m is mass of object and R is radius of planet.

Given that,  

Substitute values in formula.

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The gravitational acceleration of a planet of mass M and radius R

a = G*M/R^2.

In this case we have:

G = 6.67 x 10^-11 N (m/kg)^2

R = 2.32 x 10^7 m

M = 6.35 x 10^30 kg

Now we can compute:

a = (6.67*6.35/2.32^2)x10^(-11 + 30 - 2*7) m/s^2 = 786,907.32 m/s^2

The acceleration does not depend on the mass of the object.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y