A defective satellite of mass 950 kg is being towed by a spaceship in empty space. The two vessels are connected by a uniform 50 m light rope. The spaceship is accelerating in a straight line with acceleration 5 m / s 2. Due to exhaustion, the crew of the spaceship falls asleep and a short circuit in one of the booster control circuits results in the acceleration changing to a deceleration of 1 m / s 2. Time taken by two vessels to collide is sec.

Question

A defective satellite of mass 950 kg is being towed by a spaceship in empty space. The two vessels are connected by a uniform 50 m light rope. The spaceship is accelerating in a straight line with acceleration 5 m / s 2. Due to exhaustion, the crew of the spaceship falls asleep and a short circuit in one of the booster control circuits results in the acceleration changing to a deceleration of 1 m / s 2. Time taken by two vessels to collide is sec. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

After the mishap, the spaceship moves with an initial velocity

v_{0}

and a deceleration of

1 m / s^{2}

, while the satellite moves with a constant speed

v_{0}

. After the mishap, the two vessels will collide at a time

t

given by

v_{0} t = 50 + v_{0} t - \frac{a}{2} t^{2},

or

t = \frac{100}{1} = 10 s

After the mishap, the spaceship moves with an initial velocity v0​ and a deceleration of 1m/s2, while the satellite moves with a constant speed v0​. After the mishap, the two vessels will collide at a time t given by v0​t=50+v0​t−2a​t2, or t=1100​​=10s