A moving object has a kinetic energy of 182 J and a momentum with magnitude of 27.6 kg·m/s.

(a) Determine the mass of the object.
kg
(b) Determine the speed of the object.
m/s

(1/2) m v^2 = 182

m v = 27.6 so m = 27.6/v

(1/2) (27.6/v) v^2 = 182

(1/2) (27.6) v = 182

etc

To solve this problem, we can use the formulas for kinetic energy (KE) and momentum (p).

(a) Determine the mass of the object:
To find the mass of the object, we can use the formula for kinetic energy:
KE = (1/2)mv^2

Given that the kinetic energy is 182 J, we have:
182 J = (1/2)mv^2

Now, let's solve for mass (m):
m = (2KE) / v^2

Substituting the values we know: KE = 182 J and v is unknown, we can't determine the mass without the value of the speed.

(b) Determine the speed of the object:
To find the speed of the object, we can use the formula for momentum:
p = mv

Given that the magnitude of momentum is 27.6 kg·m/s, we have:
27.6 kg·m/s = mv

Now, let's solve for speed (v):
v = p / m

Substituting the values we know: p = 27.6 kg·m/s and m is unknown, we can't determine the speed without the value of the mass.

Therefore, without knowing either the mass or the speed of the object, we are unable to determine both the mass and the speed.