Answer:
Explanation:
From the given information:
Since both stars are in the same cluster, the magnitude and luminosity relationship can be calculated as:
Given that;
m_1 = 1 and
m_2 = 4
Therefore,
Making 
the subject of the formula:
=15.84
≅ 16
Hence, we can conclude that star X is more luminous by a factor of 16
Answer:
a) 8.61 m/s, b) 5.73 m
Explanation:
a) During the collision, momentum is conserved.
mv = (m + M) V
(12.5 g) (86.4 m/s) = (12.5 g + 113 g) V
V = 8.61 m/s
b) After the collision, energy is conserved.
Kinetic energy = Work done by friction
1/2 (m + M) V² = F d
1/2 (m + M) V² = N μk d
1/2 (m + M) V² = (m + M) g μk d
1/2 V² = g μk d
d = V² / (2g μk)
d = (8.61 m/s)² / (2 × 9.8 m/s² × 0.659)
d = 5.73 m
Notice we used the kinetic coefficient of friction. That's the friction when an object is moving. The static coefficient of friction is the friction on a stationary object. Since the bullet/block combination is sliding across the surface, we use the kinetic coefficient.
