A 2.95-kg object is moving in a plane, with its x and y coordinates given by x = 8t2 − 4 and y = 4t3 + 6, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 2.35 s.

F= 172.945 N

Explanation:

x = 8t² − 4

dx/dt = vx= 16 t      (taking time derivative)

dv/dt = ax = 16   ( again taking derivative)

y = 4t³ + 6

dy/dt = vy= 12 t²    

dy/dt = ay = 24 t   (t= 2.35 s given)

acceleration a = =

a = = 58.626 m/s²

Now F= ma = 2.95 kg × 58.626 m/s²

F= 172.945 N

luster is not a good characteristic to use by itself because luster is the property of minerals that indicates how much the surface of a mineral reflects light. the luster of a mineral is affected by the brilliance of the light used to observe the mineral surface.

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