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The Starship Enterprise returns from warp drive to
Chapter 2, Problem 83CP(choose chapter or problem)
Problem 83CP
The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 50 km/s. To the crew’s great surprise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a mere 20 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just slightly over 3.0 s. The Enterprise’s computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant.
Hint: Draw a position-versus-time graph showing the motions of both the Enterprise and the Klingon ship. Let x 0 = 0 km be the location of the Enterprise as it returns from warp drive. How do you show graphically the situation in which the collision is “barely avoided”? Once you decide what it looks like graphically, express that situation mathematically.
Questions & Answers
QUESTION:
Problem 83CP
The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 50 km/s. To the crew’s great surprise, a Klingon ship is 100 km directly ahead, traveling in the same direction at a mere 20 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just slightly over 3.0 s. The Enterprise’s computers react instantly to brake the ship. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant.
Hint: Draw a position-versus-time graph showing the motions of both the Enterprise and the Klingon ship. Let x 0 = 0 km be the location of the Enterprise as it returns from warp drive. How do you show graphically the situation in which the collision is “barely avoided”? Once you decide what it looks like graphically, express that situation mathematically.
ANSWER:
Step 1 of 4
Our aim is to find the acceleration of the Starship Enterprise as it is retarded to stop before colliding with the Klingons which is going ahead in the same direction.
The speed of the Starship Enterprise \(\mathrm{v}_{\mathrm{S}}=50 \mathrm{~km} / \mathrm{s}=50 \times 10^{3} \mathrm{~m} / \mathrm{s}\)
The speed of the Klingons \(\mathrm{v}_{\mathrm{K}}=20 \mathrm{~km} / \mathrm{s}=20 \times 10^{3} \mathrm{~m} / \mathrm{s}\)
The distance between the two spaceships \(\Delta \mathrm{x}=100 \mathrm{~km}=100 \times 10^{3} \mathrm{~m}\)
The time taken to collide the two spaceships \(\mathrm{t}=3 \mathrm{~s}\)