The 1.5 kg object is released from rest at a height of 4.4 m on a curved frictionless ramp.
At the foot of the ramp is a spring of force
constant 738 N/m. The object slides down
the ramp and into the spring, compressing it
a distance x before coming momentarily to
rest. The acceleration of gravity is 9.81 m/s^2. Find x.
Answer in units of m.

hh

Explanation:

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