To determine if the ball will reach a place 100 km away and its velocity when it reaches that point, we need to consider the concept of work done and the change in kinetic energy.
The work done on an object is defined as the force applied to the object multiplied by the distance over which the force is applied. In this case, the force applied is 1000 N, and the distance is 100 km (or 100,000 meters).
Work (W) = Force (F) * Distance (d)
W = 1000 N * 100,000 m W = 100,000,000 J (joules)
The work done on the ball will result in a change in its kinetic energy. The change in kinetic energy (ΔKE) is given by:
ΔKE = W
Since the initial velocity of the ball is given as 10 km/s (or 10,000 m/s), we can calculate its initial kinetic energy (KE_initial) using the formula:
KE_initial = (1/2) * mass * velocity^2
KE_initial = (1/2) * 100 kg * (10,000 m/s)^2 KE_initial = 5,000,000,000 J (joules)
Therefore, the change in kinetic energy (ΔKE) will be:
ΔKE = 100,000,000 J - 5,000,000,000 J ΔKE = -4,900,000,000 J (joules)
Since the work done on the ball results in a negative change in kinetic energy, it means that the force of 1000 N applied constantly is not sufficient to maintain the ball's initial velocity. In other words, the ball will slow down and eventually come to a stop before reaching a place 100 km away.
Therefore, the ball will not reach a place 100 km away, and its velocity when it comes to a stop will be less than the initial velocity of 10 km/s.